In case anybody else finds this and is trying to do something similar, I've got a slight update to offer.

I replaced the little single USB A port OTG adapter I was using behind my SNES Mini with a 3-port dangling cable version. I also read a little more on the 2-port adapter that I linked to above. Unfortunately, it does not support the SNES Mini controllers, only the Wii Classic Controllers. There must be some difference in the protocols or something, as I had assumed they were the exact same plug and protocols... I purchased one of these single-port adapters to test plugging into the USB on the OTG dongle, as they claim to also support the SNES Mini controllers. I'm sorry to say, however, that it did not work very well. The SNES mini did register some of the SNES Mini controller button presses, but they were all backwards and scattered around seemingly randomly. Then I realized that I had a couple old standard USB SNES style gamepads, so I plugged one of those in instead of the SNES Mini controller and adapter. This did give slightly better results. The keys were still wrong, but most if not all the buttons did seem to register and cause the game I was testing with to do something, if it weren't for a couple really weird swaps, it would almost be playable.

That's as far as I've gotten with this. I think my next step is to see about setting ALL the games to run via RetroArch, and binding the SNES Mini controllers with the adapters to the correct button layout.

I've also not had a chance yet to purchase and try one of the over-ethernet KVM switches I discussed above. Since my SNES mini has so many great classics on it, it will likely be one of the main devices that I use with the KVM, if I can get it to work. So I'm trying to get the controllers figured out before spending the money on the KVM switch... Besides, even if I never do get the KVM switch figured out, it will be nice to leave the SNES Mini with a clean front face and not have to pop that awkward plug out to access the ugly controller ports.

If anybody else happens to figure out the controller binding issue, I'd love to hear about it!

I bought this adapter from Amazon and liked it so much I bought a second. $20.

Works with my 2 wiitars one Win10 but two things I should note:

1. Star power doesn't work since there isn't a wiimote. You can map it to Select button
2. Whammy doesn't work. I map it to the joystick near the strum bar.
3. Cable is short, only 1 meter. Might want to get an usb extension.

Whichever way you go, rock on.

https://www.amazon.com/ELECOM-converter-Classic-controller-JC-W01UWH/dp/B009PDK6EI

I use this one and it works fine