I don't know if the system channels are as picky as IOS about being "clean dump".
If you reinstall an IOS on vWii but it's not correctly signed (fake tik, fake sign, etc.) it works but you'll have issues (homebrew channel installation error, and the WiiU mode will be unable to update the console).
So, you could try to install someone else's channel, be sure it's dumped with bluedump mod.
I don't know if "real signed" channel will be able to be reinstalled on your console, but if IOS can be shared I guess it can work.
I have HACA v6 real sign if you want to try.
I think at worst you won't be able to launch it, but the vWii should be able to read the data.
That's only supposition, I never tried to delete/reinstall mii channel.
What could be tested is installing it on Sneek !
For example, dump your vWii NAND, use it with Sneek.
on sneek, reinstall that wad and see if you can launch Mii channel on Sneek.