On a whitetail deer, I just leave the hide on it - until I am ready to skin it.
Once you have it up and off the floor on the gambrel, I just start at the rear of the deer and skin towards the head.
I try to make sure that I don't cut through the hide with the saw and only use meat saws on the meat. Keep a separate saw for the legs and neck. Keep your saws and knives clean.
Once the deer is cleaned, use a garden hose and lot's of cold water to clean out the deer - inside and out.
Before you butcher, cut off excess fat and skin that you are not going to process, along with throwing away the ribs, because it isn't worth my while to sit there and clean ribs - while the rest of the meat is waiting to be cut. When you only have a one man operation - you got to have priorities.
Then before I cut my meat, I wash it down in a clean sink and try to make sure to clean as much of the hair off the meat as possible.
Anything that is left over that I find while cutting, I pull off with my fingers and wipe my hands on a clean cloth and from time to time - wash my hands and also the cutting board. Which ends up being about every 15 minutes.
If you keep everything clean, you will not have any hair in your meat.
The same thing is true when it comes to grinding, if you clean your grinder every 15 minutes, you will not get a build up of junk inside of it.
Burning hair off the meat will transfer the smell and taste of burned hair onto your meat and will give it a funny taste.
It's easier for me to keep my meat clean and work a little harder to get the results that I am looking for than it is for me to rush to get it done and then have a big mess to clean up when I am done.