This is what I use for my overclocked SNESC. It works perfectly and I purchased both items this year. It is a combination of a simple micro-USB OTG cable, connected to good quality power supply adapter with enough current to support overclocking.
If you're only looking to connect a USB flash drive to your SNESC and nothing else, the cable I listed below will be efficient enough, even with the standard power adapter that came with your classic. Just make sure you're still using the USB data cable that came with your classic and not some generic cable (I'm referring to the one that connects to the power block). The OTG cable is pretty good quality and fairly discreet in appearance. It's also only $6.99.
The only caveat, is that it will only allow for one USB peripheral to be connected with your SNESC. So if you're looking to connect a usb drive and some USB control pad, etc, this isn't what you'll want to use. Otherwise, it's excellent.
Micro USB Host OTG cable adapter
I totally recommend this power supply. Especially if you ever want to try the Easy Overclock mod some time. However, if you have no interest in overclocking, stick with the stock power adapter for your mini. It works great with the OTG I listed above as well.
I honestly now think we were just unlucky and got a bad batch of otg cables. Someone recommended me this one as it's apparently high quality https://www.amazon.com/Rii-Firestick-Compatible-Logitech-Keyboards/dp/B07GDBPBTR but they dont post to where i live. =/
If you are a big spender, this one costs 5 cents more but looks much nicer.
https://www.amazon.com/dp/B07GDBPBTR/ref=cm_sw_em_r_mt_dp_U_Uy0nDb6RAMBZE
If all you're connecting is a USB flash drive or external hardrive (with a powered enclosure), this will work perfectly. https://www.amazon.com/gp/product/B07GDBPBTR/ref=ppx_yo_dt_b_asin_title_o09_s00?ie=UTF8&psc=1
It's what I'm using on my SNESC.
If you're looking to connect multiple controllers or additional drives, then go with the one recommended by u/rhcplive. I'm referring to the Amazon link. I would also recommend using this power supply from then on, especially if you plan to use Easy Overclock or Xtreme Overclock mod. Otherwise you may experience random crashing from insufficient power draw. I've been using it on mine and it works perfectly.
https://www.amazon.com/gp/product/B0719SX3GC/ref=ppx_yo_dt_b_asin_title_o03_s00?ie=UTF8&psc=1
I just tried to see if it would charge my phone and it does. Naturally the "quick-charge" didn't kick in, but it did start standard charging. Another way to test is to have one controller plugged into the player 1 slot & the 2nd controller plugged into the OTG cable. Just boot into stock and see if the 2nd controller is able to control the system when connected via the OTG usb slot. If not, then it's either the OTG cable - or not enough power is being supplied to the cable/system. Can you try a few different power sources to rule that out if you haven't already? Try a couple different phone chargers, the USB port on your TV if it has one, and also a couple different USB ports on your desktop/laptop. If all of those sources still fail to power the controller or charge your phone.... then it's absolutely the cables & I'd get a refund and either order the same cable I did from the link I posted above, or you can try your luck with one of these:
For the top one be sure you get the Left-Angled version. For the bottom one, Right-angled is correct. Don't know why some manufacturers label them oppositely. Shrug.
https://www.amazon.com/CHENYANG-Adapter-Galaxy-Tablet-Angled/dp/B00M7X6XNG/
or
https://www.amazon.com/Fun-Home-Female-Adapter-SamSung-Features/dp/B013ENTY9M/
Edit: Here's another cable people have had good luck with.
And you have problems with the 2A one? (That's the only one you should be using)
If the power adapter is good and the usb stick is not the problem, then the problem may be with the OTG cable
This is a high quality one
https://www.amazon.com/Rii-Firestick-Compatible-Logitech-Keyboards/dp/B07GDBPBTR