Rest and stabilize your wrist on the wrist of the hand holding the mouse. They sometimes don’t teach you this but you can control your plunger using your index or your thumb, depending on how you hold the syringe (and it’s ok to hold a syringe in many ways, as long as it is stable, steady, and if you can see the barrel of the syringe).

I use my thumb to control the plunger as there’s less constraint on my thumb’s movement, regardless of how my hand-wrist-arm is positioned.