Spear throw or a bow will help a lot with deer hunting. When a deer honks go stealth, stand still, check your surroundings and try to get it from afar.

Or just run blind and let the sloppy AI do the job instead. Sometimes they are so slow to react, you can punch them to death...

They tend to spawn always at the same spots, so you can remember the spawning points close to your base, and come back every other day knowing where they will be.