Super Mario Sunshine is not on the Wii U eShop (never released as a Virtual Console title), and Wii U lacks native GameCube backward compatibility.
Workaround (Requires Original Hardware)
Obtain a GameCube Controller.
Plug into the Wii U's GameCube Controller ports (requires the GameCube Controller Adapter for Smash Bros., or use a launch Wii with GC ports via Wii Mode—not on Wii U directly).
Correction: The Wii U does not have GameCube controller ports. Only the original Wii (RVL-001) does. The Wii U only supports GameCube controllers via the GameCube Controller Adapter for Wii U (released for Smash Bros.), but this only works in Super Smash Bros. for Wii U and a few other specific titles—not for GameCube discs or Wii Mode GameCube games.
Therefore: You cannot play Super Mario Sunshine on Wii U at all.