I have found wrapping paper at WDW, but never looked for someone to wrap a gift. my advise, pack some flat sheets of wrapping paper in the bottom of your suitcase and don't forget to pack some tape and a card!
I do know you can't find a birthday card in WDW, two years ago I was there with my good friend on her birthday, I had bought Disney dollars for her and thought I would find a great card from the world....no such luck, spent two days looking in every store. Every CM I spoke with said no, but that's a great idea...duh! (I should move to Orlando and set up a small card store!)
I finally found a "pin" card under the big hat at MGM...didn't say Happy Birthday or anything, just blank, but it served its purpose. Don't understand why they don't have someone or somewhere that would do this, as they would make a killing!
Have a great trip!