We didn't stay at a Tokyo Disney resort, but we did stay at a Good Neighbor hotel in Tokyo and another hotel near Disney. For both (and actually all the hotels we've stayed at in Japan), we booked online (we've had the best luck with booking.com) and secured the reservation with our credit card. Our same credit card was charged when we checked in. I think a Visa debit card would work the same, as long as you don't input a PIN when you use it.
That being said, it is a very good idea to have yen on you. Japan is a very cash-based society. Many places don't accept credit cards (large department stores and things generally do, though.)