I just finished reading Ina May's Guide to Childbirth. She has a great section in there on tearing (actually it's on NOT tearing, of course). If there's any way you can get a copy of that and read it before your birth, I'll bet it would give you a lot more confidence.
With my first I was scared to death of that as well-- I remember asking the nurse right away when she said she saw a little bit of head with dark hair, "Am I going to tear?!" Of course I had like two hours of pushing ahead of me at that point and there was no way she could have predicted!
I think your birth position has a lot to do with it. I started out leaning back, holding my knees back, and I could just tell that was horrible and made me more likely to tear. Hands and knees is supposed to help a lot but I HATED that, so side-lying it was. That made me a lot happier about the tearing situation-- the tissues felt like they weren't already stretched way out, so there was only the baby's head to do the stretching (she was over 9lbs and plenty big without having any additional stretching going on!).
My most recent birth was at home and I felt very comfortable supporting the tissues with my hands as the baby crowned, and I feel like that really helped (that one was a nuchal arm with no tearing), but I doubt I would have been willing to do that at a hospital in front of strangers. Hopefully you are more uninhibited than I am! Ina May says she's never seen anyone tear who had her hands down there during a birth. Maybe if you applied the hot washcloths yourself? Good luck!!