Each KTTW card can have it's own payment source. You could set your child's KTTW card with a cash back up (Disney Gift card), I believe, while leaving the credit card on yours.
You can call
DCL and have the gift cards applied to your account. Or do it once onboard. Whatever way you do it, be sure to keep ahold of the gift cards.
In the off chance that there is any credit leftover (ha, ha) DCL will apply it back to the gift card, and not a cash refund.