Here you go:
Contrary to what most people think, 99% ofd the PSX games don’t support analogs and are made to be played with the original controller. And I think on that list, only Ape Escape is the only game which requires a DualShock (can’t be played with the original controller). All other games on the list are optional.
My recommendation: Setup your controller on the core to use the standard controller by default, and then make some core overrides for specific games where you want to use a dualshock controller, like wiipeout 3 special edition, Ape Escape, or Gran Turismo.
Greetings.