Long, short story:
Am bad-to-average FPS gamer, looking to improve. Saw an OSU! gamer flinging its “shots” left and right and tried my best to mimick the experience in an FPS. And it worked significantly – all of my shots felt more “secure”, even with my aiming being rusty beyond belief.
And the “trick” to do this is simply leaving your “aiming hand” to aim (ONLY) while leaving your “non-aiming hand” to shoot and everything else. That’s it.
It’s pretty common for hardcore FPS gamers to switch their right click (which is usually ADS) from a “press and hold” configuration to a “toggle” configuration, meaning you just click to ADS, and then click again to release it. The idea is that you shouldn’t be constantly pushing down on you mouse while aiming, it creates drag and makes aiming harder.
Are you talking about remapping your mouse buttons to keyboard buttons? Seems like it would be difficult, but it’s plausible.
P.S. ADS means “Aim Down Sights”