Xibei San Ma
On the first look one might be tempted to think that Switzerland is bound to passively watch Europe burn around it. But that is in fact not true. Though Switzerland has no events at all, save for random ones, one can achieve the necessary slider moves and get into some serious Axis action by 1939. The trick is to use the (not so) random events in your favour.
The goal is to become an interventionist dictatorship - anything else is secondary - so use your slider moves to aim for that. Using the first move to become more interventionist will trigger an attack on the constitutional policy. If you cave in to the extremists, you're gonna get 2 moves to authoritarian and 2 to closed society for free. It'll change your government type from market liberal to social conservative. Also it will reduce dissent by 5%, so if you want to change any ministers, do it beforehand! Starting from 1937 you should go for authoritarianism. It might trigger some more "random" events (normally an economic policy initiative, because you are still at 7 for free market). You should always choose the option that makes you more interventionist and/or authoritarian, even if you have to pay the price in dissent. But if you don't, you won't be able to go to war in 1939. You will spend most of the time paying down DOW dissent anyways! If you want to devise a clear "random event" strategy, you can look up the conditions for the events in the ML or SC Events file in the database directory.
Switzerland has some ok ministers with more becoming available as your regime changes. Go for everything that ups manpower growth, foreign manpower use and IC bonuses as well as less supply consumption, etc. If you play as Switzerland, you probably already know the basics...
Disband your starting infantry! You won't need it until 1939, so why pay for support and upgrade? Switzerland severely lacks manpower and cannot afford to use simple infantry anyways. Tanks + planes + specialized and/or very agile troops together with brigades are the way to victory. It might be advisable to keep the mountaineers and the bomber though. The bomber will let your Air commanders gain some badly needed experience and the mountaineers are a great asset in conquering northern Italy, eastern France and Spain. BUT DON'T REINFORCE THEM YET! That'll only cost manpower and IC just so you can pay more upkeep for them uselessly standing around for three years.
Using sturdy troops also means that you will rather upgrade your troops than build new ones because of the experience. Switzerland starts with a completely drafted army. You don't really need to change that, just try to produce long chains from the start. You need to plan ahead for that, because if you stop production due to lack of IC at some point, the chaining bonus will be reset. Also you don't want to produce a lot of troops that you'll have to disband later anyways.
If you only focus on one troop tech branch at the time (which doesn't mean that you should research in advance, also you will attain many blueprints ), you can skip one or two upgrades. This way you get them nearly for free. This applies especially for troops that don't go into dogfights with the enemy - bombers or simple landgrabbing/encirclement cavalry.
DON'T USE MILITIA!!! They serve defensive purposes and defending is not the strategy you should apply if you ever want to be more than a little spot on the map! If you must, use Garrisons combined with brigades, but you should rather go with some mobile QRF. You won't have Air Superiority since you are playing Switzerland and you'll eventually crush one backbone of the original Axis - Italy. The main problem for you is to secure your gains in Italy, France and (at least until you puppet it) Spain. If you send weak troops to garrison the beaches, they're gonna be bombed into oblivion and/or drain your oh so precious manpower pool! They don't need to deal damage or "win" those bombardment battles! They only need to hold their ground without loosing strength!
Don't worry about TC and Org.regain for now! Italy and France aren't the SU. One or two really good encirclements are enough to deal them the fatal blow. So it's sufficient if you start out with full Org. and don't squander it in useless attacks.
As soon as you join the Axis and get german blueprints, abandon the superior firepower doctrine and go with the german Spearhead. You'll get all the blueprints from Germany, you have just the man to research it (Henri Guisan) and it fits your (mainly for manpower reasons) tank-based warfare perfectly.
First years are solely IC production, start it in all 4 provinces. You won't be able to produce it all immediately, but that is the only way to get some halfway decent base IC allowing you to have a 2nd research slot before you start to conquer.
Once you are near the year 1939, you should think about producing troops. You have to start earlier, if you disbanded your Mountaineers, or a bit later if you kept them. Continuous IC production (with a chaining bonus) is also a possible way, if you kept your military intact. Especially in easy mode that strategy will pay off, since it efficiently increases your base IC.
As soon as your economy is up and running, you can exchange some supplies for resources to assure continuous production. UK is the best partner for that since you start with the same government type and you can boost your relation up to 200 with trade only making the possible deals better for you. USA might be a good choice, too.
You should also get some trade deals with Germany. Depending on which alliance you want to join (I recommend the Axis for the fun and the fitting blueprints) you might have to set priorities. Once you start troop production, build tanks and some fast troops.
Until 1939 your research should be focused on IC and manpower generating techs (again don't research in advance!). Also you should make sure that you can produce a somewhat modern army by then. So some newer tank technologys are also necessary. In terms of brigades you are fine for now, since Switzerland starts with some research progress in those.
Don't do aerial research at the beginning - your allies are gonna give air cover for you anyways. Save that for when you actually can accomplish something in the air. In terms of Land Doctrine go for Spearhead, but don't research it before you have the blueprints; that would simply be a waste of precious research time.
Aerial research should be focused on TAC/NAV and Interceptors.
Naval research and production can wait for now, you don't have a port to deploy anyways. Once you do it though, you can either try to follow in Germanys footsteps because of the blueprints or go for Carrier Warfare and try to steal blueprints from UK/US/J because your Dornier Tech Team is pretty good at researching Carriers (at least for a country that is miles away from any port). No matter what you do, the Naval Doctrines are gonna prevent you from being a naval superpower.
If you play with tech team takeover, that problem is probably gonna solved, but that would kinda spoil the fun of having a Carrier fleet flying the flag of Switzerland dominate the Mediterranean Sea in my opinion.
I'll only describe the one I used, I'm sure there are a lot more.
I broke the german event chain by joining the Axis after the Anschluss and before Munich (after Munich and before the attack on Poland might have been more feasible for Germany would have been a bit stronger). I boosted my relation with them a bit and was immediately accepted. To prevent Italy from joining the Axis and thus keeping me from any expansions and to gain a stronger economical base, I DOWed Italy. Now here's a trick: A quick armored strike through Milan to Venice and then north assured that every province conquered by the Axis fell to me and also encircled a few Italian divisions. And once Germany got his army down through Austria, he basically did all the work while I reaped the rewards.
Once you get into the inevitable war with the Allies you can apply the same strategy to France. If everything worked out ok, then Belgium and Netherland are probably still alive and they're gonna stay that way. But you're gonna provide Germany with the needed route into french heartland, so you're gonna win eventually against France. Make sure that France goes to YOU - you'll need it to conquer and puppet Spain and Gibraltar.
Don't puppet Italy, since it's your gate to the west.
If you DOW Yugoslavia, you're gonna trigger the events leading to Bulgaria and Romania joining the axis. You don't want that to happen.
So as soon as you feel strong enough to take them on, DOW those two beforehand. Take your time, they can't reach you except with planes. Don't forget to pay down the dissent as it impairs your fighting capability and raises partisan level which in turn hampers your TC and might lead to partisan revolts.
Once you got a puppeted Nationalist Spain and conquered those three in the east, you might wanna go for Turkey, you could also swallow up Hungary and/or Albania before.
Once you have Turkey conquered, you control the Marmara Sea and the second entry into the mediterranean out of three. And you have then got an unblockable continental supply connection into the Middle East: Suez here we come.
At some point sooner or later you should start to research maritime technologies. Get blueprints from Germany and go their way or try to spy on Britain/US/Japan (whoever seems feasible for diplomatic and tactical reasons). Germany will need your assistance at sea.
From there you're free to go wherever fate takes you, be it Africa, Persia, India, China, Russia or Overseas. If it makes sense, puppet some bigger countries like the Ottoman Empire, Nationalist (or Republican) Spain, Hungary, Bulgaria, Czechoslovakia etc. You might wanna consider boosting their base IC by building some in their provinces. Since they start with the same techs you have, they could possibly (don't count on it though) help you with your Naval Doctrine Research. And they can do so more effectively with a third research slot. Also it helps them to keep up with the technological pace and be more than cannon fodder. But don't forget one thing: They need Resources to keep their industry running, and since they are your puppets, they need to get them from you. So make sure you fill up their gaps in resource supply by "trading" them some of yours. You can't use them all anyways because of the foreign IC rule.