Hey, I'm interested in trying to run MM. I own a Wii U, but not a Wii any longer. Would running MM through the Wii U's Wii mode VC be equivalent to running it through a regular Wii VC?

Yes I have a wiiu and I install the wii vc in the wii menu and it works. I recommend you to watch a tutorial to how to install hombrew channel in a wii because the wii menu is the same as a wii.