Work on the stuffing box while the boat is in the water
I have never tried this, but it was suggested to me:
Go the hardware store and get one of those wax gaskets used to install a toilet. Break out the mask and snorkle and press this gasket around the prop shaft where it exits the hull. When you are done remember to turn the shaft so the wax falls off.
You could also just turn on the bilge pump and work fast. It is scarey but I''ve repacked my stuffing box like this.