The IC is a custom (or relabeled) Nintendo chip marked "WCRX-DOL / T2.7488K1". ("Wireless Controller Receiver - Dolphin"). It is presumably a microcontroller that decodes signals from the radio and sends them to the console.
This 4-pin connector goes to the joypad connector on the GameCube.
Desolder these four points to remove the shield and expose the radio on the other side.