Not sure about pre-paying (although would think there is a way), but once you get on the ship, you can take them to Guest Services (the "front desk") and they will immediately apply them. When we were on the Fantasy a couple of weeks ago, we had both a Disney VISA rewards card (to redeem our points) as well as a VISA debit/gift card that we received as a gift, and the front desk was able to apply both to our account immediately. I took them down at different points during the cruise (for no particular reason), and when I took the rewards card down, they had already charged our credit card for everything done through that day, but applied the rewards card to our account and credited my credit card for the same amount. With the debit card (much smaller amount), they simply applied it to the account, so we had a credit (for about 15 minutes until we hit the gift shop...again!).
In other words, unless there is a good reason for doing it ahead of time, it will only take you a few minutes to get them applied to your account once you're on board.