Pretty much every big bank has foreign currency accounts. However they may be somewhat specialized towards electronic transactions and investments - I do not know the fees involved, whether they actually have cash on hand and so forth.
Which leads to the question of whether it makes any sense at all to open a USD account in a country where banking fees are traditional in order to store "a small amount". But that isn't the question that the OP asked.
Cr Suisse has US Dollar accounts, no questions asked as far as we were concerned, but then we are not American.
We can transfer funds between accounts and you can choose the currency for the transaction, their online banking system works very well most of the time and once to you get used to it.
From personal experience, UBS, CS, BCV no longer allow accounts for U.S. citizens not living in Switzerland. I own a vacation condominium in Switzerland but it made no difference.
UBS dose for sure offer USD accounts charge an annual fee of about 20 or something like that chf. The idea is to transfer to money onto it and out of it not really to pay in or withdraw, but you could still do so i think for a 2 percent fee (i guess thy also have a minimum charge ie if you put in 50 dollars you might have to pay the minimum fee of 20chf...
IF you still have a US address, you can keep an account at Chase. Chase has online banking with international transfers incase you need to transfer funds.
And yes I have noticed all banks here also allow foreign currency accounts so USD account should not be a problem if they don't have a problem taking on a US citizen. I am with Migros bank and it works for me.