Look at your black grounding wire in the photo above. The set screw brushing the wire on the left side of the picture is screwed into the coupling, perpendicular to the shaft. That presses a rectangular piece called a Woodruff key into the shaft and also locks the shaft to the coupling. If you are going to remove the shaft from the boat, or remove the coupling from the shaft, the set screw will need to be loosened - you might as well remove the set screw. If by some miracle you do not need to do this, the set screw does not need to be disturbed. You probably can’t remove the shaft from the coupling just by releasing the set screw and pulling out the shaft.
The other bolt touching the ground wire in the photo is one of probably four shaft coupling bolts that need to be removed. They screw directly into a threaded piece called the engine coupling, which doesn’t need to be disturbed. Once those bolts are out, nothing is holding the shaft to the engine except - possibly! - rust.
If you’re disassembling all this you may decide you want to refurbish the shaft packing gland, maybe replace the shaft itself, etc. (note, shafts are not that expensive.) This will require removing the shaft from the coupler, using whatever home-grown press device you can maneuver in place. Lots of discussion on how to do that at the moyermarine.com forums. Your boat seems to have pretty clear access to the coupling, which is good. My boat is a vee drive, and does not. Squeezing the coupling off the shaft in those conditions is probably the single worst job I’ve had to do on the boat.