If you're that paranoid, get a debit card. Something like a prepaid card with a set amount of money on it every month only for therapy and nothing else. Most places use the term "credit card" generically when they mean any credit/debit card.

Another option would be seeing if they accept online payments. If so, see if your credit card issuer has a service to give a virtual card with a different card number. I know Capitol One has a such service and I use it regularly.