Modern mice have two buttons, usually three, and most of them have wheels. I think with that combination of buttons you should be able to contain the lock picking mini-game entirely to using the mouse. Perhaps move the mouse back and forth to adjust the angle, and scroll the wheel up or down to turn the mechanism.
I find it somewhat awkward to use a gliding mouse for one rotational motion, and a dichotomous set of keys for the rotation. It doesn't feel correct.