Not Playable. Toy Story 3: The Video Game (Wii) requires Nunchuk for core movement.
Without Nunchuk, you cannot move your character. Menus navigable with Remote only.
Cost: Used Nunchuk ~$5–$10. Classic Controller Pro ~$20–$30. Highly recommended for TS3 and many Wii games (Mario Kart Wii, Brawl, Monster Hunter Tri).