You can test mouse/superscope recording in
this Snes9x; it's not an official version and probably can't be accepted for publication (due to incompatibility and emulation inaccuracy issues), but the next official version will record mouse input similarly, barring any major changes before its release. The only mouse-related change already made after that version is to allow you to use the keys or joypad buttons assigned to the SNES controller (like A and B) to activate clicks and triggers, or autofire/autohold those buttons, instead of having to click on your actual mouse each time.
The game has to be running to see where the mouse will go, so the way to get instant and precise movement is to put the mouse where you want it to go, then load a savestate and frame advance, and the mouse will teleport there. Moving it near the edge of the screen can be tricky because any input that accumulates to put the mouse outside of the screen will be entirely rejected until you move it back inside and try again, or at least that's what Mario Paint does.