I wonder if we can use some 3rd party program on wii (like nintendont, devolution) to speedrun gc version.

Maybe these posts will help your answer:

https://www.speedrun.com/re4console/thread/2yu34

https://www.speedrun.com/re4console/thread/oz22t

EDIT: It would be interesting for moderators to add in the rules that emulators are prohibited and put the reason.

My answer is: No, emulators are not allowed unfortunately, more softmods like nintendont is the same only that you are using an application made by the internet community INSIDE the console.

To run RE4 on the Wii, you can only use the disc version (for Wii or GCN), USB/SD loaders to boot the game are not allowed.