It doesn't have an SD slot though, which makes it borderline impossible to hack with software alone.
Exactly, you can't hack it if it essentially does nothing to begin with.
Nintendo basically set the Wii Mini up as a closed-loop. There's no way to input data. There's no way to output data. There's just nothing in general. Only official software runs, and only from the Wii-ROM drive. There's no internet access, there's no Shop Channel (Even before the service was shut down), and there's no other exploit vectors. You can't run modified games either, as that requires the signing bug to be present at minimum, even with a Wii-ROM emulator. It just doesn't work, period. It's barely even a Wii anyway, so it's probably best that we forget about its existence.