I'm using a NES/SNES Classic power adapter after numerous reports online that it works fine. No troubles to report.
That said, this doesn't match what the manual wants. This was about 5 days ago when mine finally arrived and I hooked it all up (So the numbers I'm about to quote may be slightly off), but I believe the manual says 5V/2.0A and this adapter is listed as I recall at 5.3V/1.0A. But it was reported as working in numerous places and that's holding true for me, so I'll stick with it rather than seek out the hard to get official Hori adapter.
As I recall from a random thread I stumbled across a day or so before my TG16 Mini arrived, it sounds like too much amperage is possibly what has bricked some of these units. Several people said they tried to use a Rasberry Pi power adapter with 5V/3.0A and had a non-functioning controller port upon powering up the system.