Welcome!
I was on the other side. I was balding and started going with shorter and shorter cuts until I started using clippers at home (actually my wife clippered it for me). Everytime I decided it should go shorter, it always took some convincing to get her to be good with it. I'd often joke about shaving entirely - this usually helped to get her to go along with making it shorter.
After clippering for awhile with no guard, finally went fully shaved.
If you are having trouble convincing him to shave it, you could try the clippers route and gradually go with shorter guards.
