WiiSX is a PSX emulator for the Nintendo Gamecube & Wii brought to you by Wii64Team (emu_kidid, sepp256, tehpola). It is based on various PCSX code bases, see the credits section for specifics. The emulator can be controlled with any combination of GC controllers, Classic Controllers, Wiimotes with Nunchuks and even just Wiimotes. See the included readme for details on the controls. You can load ROMs and saves from a FAT formatted SD or USB (details on the folders required are in the readme).
Full details https://wiibrew.org/wiki/WiiSX
We do not have a seperate games list for the PSX as there are only a few games on Now Play, however you can get more from the internet, so have a loot at this list and see which are compatible with the emulator.