If you are staying on property you can always go the concierge desk in the main lobby and ask them to print you a copy of your reservations. They do this for free and, as far as I know every resort from value on up has one (not sure about DVC). We've done this many times ... this past summer at CSR our reservation list even included our backstage magic tour and wishes dessert party.
I've never been asked for my ressie number, just the name and then they confirm party details, but I figured it's best to have the number with me, just in case.