I want to do an Any% and 100% Speedrun, but, the problem is, I can't/don't know how delete my save file or find New Game. Is there anyway I can try doing this on my Wii or do I have to get myself the Xbox 360 version and do both runs on that?

From my experience in the game, the only way to delete save files off of PRR is by going into the Wii's Storage Memory and deleting the data file off of your system. I have to do that on the Wii U as well and it's so backwards, but that's what you have to do.

https://support.activision.com/articles/en_US/FAQ/How-do-I-clear-outdelete-the-saves-for-the-game-on-Nintendo-Wii

The website sorta helped me. It didn't say I had to go to Wii Manager. I've figured it now. (It should not say Channel.)