i know this , im talking in theory here not practice
How about a good old internal modchip, and start playing burned backups on that thing ?
I got my Wii back on launch day in 2006 and shortly after I installed myself a Wiikey in it, and it was like $12.
Then I've been burning my games for years.
This, was way before the Twilight hack and USB loaders.
I waited and waited until the USB loaders got so advanced that it was actually a great improvement to play the games off USB than the optical disc.
But my Wiikey is still in place and still works ! In fact, I had to burn and play some games because they were tricky to lauch from USB at first ( like Metroid Prime Collection, and also the dual layer Other M wasn't working until somebody found a hack ).
Also Rock Band 3 seemed to play better off the Disc, because of some USB instruments recognition.
All in all, I'm very satisfied with it and I'd never trade my Wii for anything else, considering that with my setup, I can flawlessly play any Game Cube game as well !
So to the original question.
I'm not too sure if anybody bothered to look inside a Wii Mini, but if anything fails, one could still go for the hard modchip route and play games off the disc drive as it was meant to be ! A throwback to the past in every way
Not that I need one, just saying.