Creating Foreign Bank Account for Access to Foreign Currency

Your question seems a bit vague but TransferWise is a good option for flexibility with multiple countries:

A TransferWise multi-currency account lets you keep money in more than 50 currencies, and convert between them at the real exchange rate whenever you need. It’s free to sign up and there aren’t any subscription fees.

You can also get bank details for GBP, EUR, AUD, NZD, USD, and SGD (with more currencies on the way). Share these details to your friends, companies or customers in order to receive money from around the world.

What you also should consider is, that in Switzerland the local currency is the Swiss franc and not the Euro. So the Euro is foreign currency there as well, that would kinda eliminate what you want to do to a certain degree. If you want to get Swiss francs that would maybe help.

Also the (total) privacy of swiss bank accounts is mostly history, especially if you have a small budget. And small meaning below multiple millions at least.

I think you can easily find an American bank that let's you hold foreign currency there, that might be a lot easier to manage it with little to no disadvantages.

I myself have a Swiss bank account while living in the EU, because i work in Switzerland and earn my wage in Swiss francs. This way I can convert whenever I want to Euros and hold the risk and the benefit of exchanging at will and not at the date of the paycheck.

Aaron, do not get scared by other answers. Obviously there are risks involved, but you can manage it if you are cautious and watchful.

1. Note that fairly nobody is using checks in Europe anymore. Everything's done here via SWIFT, SEPA or local domestic transfers. All banks support all three methods while the local one is usually free of charge.
2. I live in Poland and my local Citibank offered me a "global account" that basically meant that they would open an account for me not only in Poland, but also in US and other countries wherever I like in almost any currency - I checked PLN, USD, CHF, EUR and GBP and it was ok.
3. I also have a CHF account in Switzerland, however the charges and negative interest rate (yes! you pay them for keeping your money!) make me to seek for an alternative.
4. My local bank offered me also "multicurrency internet exchange account". Once you file the papers it is one click to get an account in the currency you like on the 0-0 basis - no interest no fees, free transfers up to certain limits, rather low spread (not the best on the market however). In the pre-covid era you'd needed however to visit a branch so they can verify your identity. Not sure how is it now. The bank earns on the active traders so you need to be prepared for occasional call proposing leverage, forwards, options, whatever. Do not follow blindly and do not use this instruments if you do not understand how they work.
5. An important advantage of EU banks is that by EU law each member state needs to guarantee consumers' deposits up to the certain limit that varies from country to country. Not sure however if it is applicable to non-EU persons as well may not apply to Swiss accounts, as it is not part of EU