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.
When I play FPS, I bind movement to SDF, jump to A and forward to the right mouse button. That allows me to control aiming and forward movement with one hand and to squeeze the mouse with the whole hand when shooting to avoid jerking. WASD is a silly scheme in any case, I don’t understand why it is a default.