If I flesh and thin by hand, I like a small curved bladed knife that will fit my hand. And old (must be sharp) curved bladed butcher knife works well for thinning/shaving. Placing a piece of 2x4 or 2x6 under the area of the hide you're working will help you greatly.
Another trick you can use to thin a hide down is, build you a 6x8 foot frame of 2x4's. Flesh, pickle and tan the hide as usual. Allow to drain. Lace the deer hide onto the frame using clothesline (I use parachute cord) and small "S" hooks, stretch it tight. Allow hide to completely dry. When dry use an electric sander, and while being extremely careful, sand the hide thin. Any holes you may cut can be repaired later. Take the hide down, soak in a bucket of salt water until pliable. Rinse and drain. When drained, apply your softening oil and proceed as usual. Remember, the thinner a deer hide is, the softer it will finish out.
If you need more info, shoot me a PM and I'll give you my phone number and you can give me a call.