Do you know the guy well?
It might be worth making an appointment one evening well before the flight, to get to know each other without any pressure. That way you can judge whether he's going to be a flight hazard, and he can get comfortable with the idea of flying with you, and the things he can expect.
If you only meet the guy an hour before going airborne, there might be too much pressure to make a sound decision. And for him too much opportunity to become nervous.
Depending on the outcome of that meeting, you might want to consider removing the stick from the pax seat, if that's possible.
Personally I wouldn't have a problem with a pax with mild Parkinson, as long as his uncontrollable movements don't lead to an uncontrollable grasping of the stick (or rudder!) Then again - I fly side-by-side seaters only so if necessary I can just whack his hands from the stick.
And the usual caveats about taking pax on aerobatics rides apply all the same of course.