Marcie - as a former travel agent over the years I experienced a number of tour operators who would want a photocopy of the front of a credit card to protect them against fraudulent use. I don't remember if they also wanted the back side, but that's where the security code is located, but they may also want to verify the signature.
I would check them out - also, if they check out OK, you might want to see about doing a wire transfer in lieu of using a credit card.
As a final comment - you could just fly there, get the hotel to handle your transfers and set up any tours you want to do at the Falls.
----
Leslie