Also Woody could history wise align the story with KH anyway with or without powers. Since according to the creators "The story in the Toy Story world will take place after Toy Story 2, and will follow its canon timeline rather than taking place in a parallel storyline." Source.
But that's up the mods to be allowed, I know I was able to so it in the Paixao game with Aladdin so he'd know who Sora is. ^^