The only non-essential thing you can remove is the disc drive. The Bluetooth module and the Wi-Fi are both needed without software modifications to the Wii. You can play GameCube games through
Nintendont without a disc drive, but playing Wii games without a disc drive requires use of emuNAND to emulate parts of the drive in software.
Since you're working on portablization, you would benefit from using a package called "portablizemii" available at BitBuilt.net. It offers a software solution that removes the need for the Wi-Fi module and disc drive (Bluetooth is still needed) and it makes Wii and GameCube games very easy to play with an all-in-one interface.