There are a few places that require a credit card...Chef Mickey's is not one of them. I called yesterday because I wanted to see if I could luck out and find an earlier dining time for our upcoming trip at CMs and the lady let me know that most people do not call and cancel those ressies because there is nothing binding you to them.
So I guess it boils down to no you don't have to use a credit card and technically you don't have to call and cancel. But as a person looking for ressies at a booked up time it is nice to call and cancel if you know you aren't going to be there so another family can get in.
ENJOY! Chef Mickey's is a great time and I am sad that we might miss out in our upcoming trips...