At DIII, if I redshirt a player what (if anything) will it do to his WE or the likelihood of him leaving the program?

Very doubtful he will leave the program, but the impact on his WE can vary.  If you didn't notify him during recruiting that you intended to redshirt, try putting the shirt on him before your first exhibition game.  If he complains, take it off but don't play him in the exhibition (remove him from your depth chart and set him to "Mop up").  Then try putting the redshirt back on him.   Rinse and repeat.

I'm not sure about the number of times you can try this, but the few times I've done it, they usually accept the 'shirt after the 2nd or 3rd attempt.  If not then, then expect his WE to plummet if you keep the 'shirt on him.

Yeah I just got a recruit and I didnt mention anything about redshirting and the first time I tried to redshirt him he took a major hit on his WE and told me he thought he had a shot at playing some major minutes. Thats when I took the redshirt off of him and his WE returned to the same. That is when I put the redshirt back on and in a bit I got a message that he said he was all good about getting redshirted and nothing happened to his WE or anything else.

Coach calls and scouting reports sometimes can give you an idea if the guy is likely to accept a redshirt.  I think rides the bus and doesn't care of back-ups play types pretty much always accept a redshirt (certainly D3 guys), wants the biggest of everything types can be a question.  And Randolph Macon still sucks.