The problem is that sending money directly between accounts is the normal way to do it in Europe and is cheap. I can log into my online banking and send money to any account which has an IBAN (International Bank Account Number) in any currency I like. They have probably just assumed you can do this.
My guess is the account number they have given you is an IBAN.
If you do send money, do it in Swiss Franks (abbreviation: CHF, not CSF). If you send it in another currency they will have to pay a few Franks to convert, so to be polite you would have to add the cost of the conversion to the amount you sent.
If it is too expensive to send direct from your bank account, then giving them your credit card number is a good idea. Since the sent you the item without getting money up front, they are obviously honest.