Emulator runs are now allowed on the leaderboards.

You can use Dolphin 5.0 to play the Wii version. Dolphin loads faster than any legitimate platform, therefore emulator runs will remain hidden by default but can still be submitted without any issues.

Further, you may submit runs emulating the PSP version using PPSSPP 1.12 or higher. Due to some changes to the PSP version, it is unlikely that any outrageously fast runs can be done either on emulator or on a real PSP.

EDIT: Emulators are now shown by default. If people ever start to care about loading advantages, feel free to start doing loadless timing but overall there doesn't seem to be a strong necessity for it, considering the game only has few runs.