I'm new to Animate, so here's a question.

Just to add to @kglad's suggestions:

From what I've read, Lazy Nezumi can work with Animate.

https://lazynezumi.com/

Personally, I have not used it, but you can install the trial version and see for yourself.

you can adjust the sensitivity of the mouse (to hand movement).  that would be an os setting and apply to all mouse usage in and outside of adobe apps.

to learn how, google your os and setting mouse sensitivity.

or, if it's worth it you could consider a computer accessory, a drawing tablet though i would think if your hand is too unsteady for mouse usage it probably would not be better with a pen and screen.