It's been a few years since I hacked my wii. It was probably like 2018. I used an exploit called 'letterbomb'. You just put the file on your sd, then the console thinks you have a message from another player, you open the message, and it runs the hack. I'm not sure if the process has changed since then

https://wiibrew.org/wiki/LetterBomb

The hardware between the wii and gamecube is pretty similar. Wii runs gamecube games natively rather than through emulation.

If you use Linux on your computer, there's a tool called 'wit' (Wiimms ISO Tools) for managing wii and gamecube roms. Check your distro repository.

The cool thing about wii discs and that they all have a hash signature from nintendo so that you can verify if they have been tampered with. This was intended to prevent people from running authorized code on the wii console, but tools like wit can use the signature to make sure the game has not been modified. The signature verifies the game partition on the disc, so it even works on compressed discs.

IIRC I used an app called 'Nintendont' to launch gamecube games on the wii from a usb hard drive.

You can download wii and gamecube roms from https://vimm.net/ .