If the gift cards are Disney ones, the credit card company isn't likely to accept them as a form of payment.
Just to be clear, when you have a room only reservation, the balance owing on the reservation must be paid in full at the time of check in. You can pay it off in advance if you want, using credit card, debit, or gift cards. If you want to pay it off with gift cards on arrival, don't give them your credit card number for the online check in.
That's not the same thing as charging privileges after you have checked in. If you use your magic band to charge a purchase or a meal, that charge goes onto your resort account. When the account reaches or nears the preset limit, the credit card will be charged for that amount, and your room account is zeroed out. If you don't want your credit card charged, you need to go to the front desk and pay it off with your gift cards instead, BEFORE they automatically charge your card. You can get a print out of your charges at the front desk any day, to keep track of your spending.