Your best bet is to ring some foreign institutions, either their offices here (if they have any), or directly in the countries. You will not need to go off with a suitcase full of money, and a euro transaction will not cost any more to send abroad than it would domestically.
One of my foreign accounts is with Keytrade Bank in Belgium. They are a bank and stock brokerage, but you can just avail of their savings account if you want. It was very easy for me to set up at the time. Offshore accounts are very common, especially in Switzerland, so I don't see there being much of a problem for you.