Cold water shavers use cold water to wet their face then apply creams or soap. I tried it once and had the absolute harshest shave ever. Don't let my opinion sway you though and give it a try. I just think that if the rest of your shave is OK, then it might be technique.
I found that inflating my upper lip and pulling my nose up towards my eyes really help. That way you can maintain a good angle. If I was going to bleed it would be around my nose. Knock on wood; as long as I am pulling my nose up and inflating my lip it has been good.