The motion for pitching a baseball is actually much more unnatural than pitching a softball.

and yet...arm injuries for pitchers are quite uncommon for softball players. ( knees and throwing injuries for infielders and outfielders are much more common.) there is some schools of thought that young baseballplayers should throw underhanded until 14 years old.

I have been a fastball pitcher for about 10 years. Other than a minor rotator cuff problem I have not had an injury at all. One thing that both my massage therapist and chiropractor noticed is that the shoulder of my pitching arm is rotated slightly inward (they tell me it is nbecause of my pitching).

As long as you have proper technique, I would think that the risk of injury would be fairly low.