All banks and bank-like institutions you might have access to will comply with the same anti money-laundering and know-your-customer regulations. It's not really up to the individual bank to decide.
The "Swiss bank account" is largely a thing of the past, as they are forced into data-sharing agreements with the United States and possibly others. And even so, you need to be a Swiss national to qualify for a bank account there.
You can use cash as much as possible when it's an option, of course. It's less convenient, but privacy often is.