Prednisone made my hair awful on my face, haha. I sounded gross just saying that so I apologize, but it sounds like everyone has had the same problem. I had to wax ALL the time to keep it managed. Finally I bought some of those straight razors and I would shave when I didn't have the time/energy to wax.
I went really far out and bought a Tria laser, which would recommend, but you will probably be done with the pred and the hair growth will slow before you would have results from the laser. Might not be worth it to you to spend so much money on a laser anyway. It hurts bad too. I actually don't use mine enough. I am a big wuss. Actually this post has made me want to fire up my laser.