I think it would be a bad idea to run that engine without a governor - it won't be protected against over-revving and it won't respond to load. B&S engines are already a bit prone to throwing connecting rods through the side of the crankcase even when you don't remove their safety system that tries to prevent it.
The governor is not very complicated - there are only about three parts in it. If you are having problems with the engine hunting - that is cyclically speeding up and slowing down without you adjusting the speed setting - it is not a fault in the governor, it is just lean mixture, and that is easily adjusted with one screw. I suggest you describe your issues, and see if someone can suggest a way to fix them.
