Which emulators are allowed for this game? Been practicing with the SNES9X core in Bizhawk, but figured I should probably get some official confirmation. I looked in the guides and and the game rules but didn't see any. The closest I saw was that ZSNES doesn't emulate the game properly.

Bizhawk is a great choice (if your PC can handle the software, because it takes quite some resources :D). Snes9x or BSNES as core are both totally fine, though BSNES is said to be more accurate. And yes, maybe some mods could update that section @Cliqz ;-)

How about the SNES Classic? I think it's possible to use the canoe emulator to run the game on the classic. Is that allowed?