I could be wrong, but I even if I did not want charging privileges, I always had to leave one on file just in case, for any damage etc
Not true at WDW resorts, which makes them a little different from most hotels. They already have cc info from when you paid for your reservation if you trash your room.
OP, if you have booked a package vacation, this won't be a problem, since you will have already paid in full for the reservation before you arrive.
If you have a room only reservation, then the balance is due at check in, unless you have chosen to pay it off before arrival. You wouldn't HAVE to pay it off using the initial credit card- but you would have to have something - debit card, gift cards, cash, or another credit card- to pay off the balance due.
If you are talking about charging privileges, again a credit card isn't mandatory. You could give them cash, gift card deposits or your debit card instead. Or you could just not have charging privileges and pay for everything OOP.
Personally, we would never dream of travelling without a credit card. Even if you don't use it, it's a much needed safety cushion in case of an emergency.
