Going through our Softmod Any Wii guide in full will overwrite everything in the system so it should play all disk-based games as if it is on a non-modded updated system, plug be able to access any other homebrew apps and features that you would want (USB Loading, etc).
The guide is linked in my signature.
You will want to do everything in chapter 2: ModPack, IOS Update, Shop Channel.
Menu to 4.1 is optional if you have 4.x already, but if you have 3.x, you should install it, then install priiloader and configure as recommended by the guide.
Dont' just do chapter 2, though. Do everything from the top. Chapter 3 will give you current apps to run in HBC.