You cannot plug a GameCube controller directly into a Wii. The ports are different:
GameCube has **no "paddles."** It has a standard stick, C-stick, A/B/X/Y, L/R (analog triggers), Z, Start. "Paddles" usually refers to **back paddles on modern pro controllers** (Xbox Elite, Scuf, DualSense Edge). If you mean the **GameCube controller itself** — see above.
Before buying adapter: Search "Game Name Wii GameCube controller support." Many Wii games **only** support Wii Remote (+ Nunchuk/Classic).