I went through this last spring. My advice is to go through it all, if you haven't since you got the boat and make sure everything is right. Advice to look at the engine beds / mounts is excellent. Do you have a vibration problem now?
If you replace the coupler and have the shaft and prop rebalanced by a marine machine shop it will likely cost you as much as new parts will, or at least so close that the pain and suffering you will likely go through to get everything apart won't be worth it. If I had to do it again I'd order a new shaft, coupling (split, as they are much easier to deal with), bearing and stuffing box hose (make it high priority to replace this while you have it apart). Then I'd take things apart by cutting the shaft in half. I spoke to the folks at the link below and they were fantastic on the phone. Very knowledgable. However, I took the advice of a Captain I ultimately hired to help me bring the boat around and went to a marine machine shop in RI to redo all the old stuff. They were great, but the tab, as I said, plus the effort (two hour plus round trips), makes new stuff on my door step more attractive to me if I had to do this again. If you have a good shop close by it may be less attractive to you.
http://www.deepblueyachtsupply.com/
Don't get me wrong. It is certainly possible to press the shaft out of the coupling and to run back and forth to the machine shop. It is just a pain and it would have been far more cost and time effective for me to have cut it out and had the new parts show up on my door step UPS. Getting the prop off was a pain too, in my case. I don't think it had ever been off. Someone recommended using tef gel when assembling. I will certainly try that the next time. Broke three prop pullers, resisted all attempts to lubricate and heat, then managed to ease it out while still on the shaft past my rudder (thank God) only scraping the paint on it a bit. Once out it was a piece of cake to remove. I put a piece of PVC pipe of an appropriate diameter in my B&D workmate, slide the prop and shaft in and whacked it with a hammer...something you don't want to do while it is attached to your transmission by the coupling...and it popped right off.
Cutless bearing replacement was the easiest part of the job. Threaded rod, a couple of nuts, some lengths of pipe and appropriately size washers and a half hour tops. I took the advice of others and put the new bearing on ice before using the press I made with slightly larger washers to pull the bearing into the skeg. Piece of cake. Had to do much the same job replacing bushings on the torsion bar front suspension of my 64 Dart GT convertible.
Ultimately it was a good experience doing it all myself. I hadn't had an inboard before and the job was quite daunting to tackle while still very much new to the boat. I am certainly a better marine mechanic for the experience ;-)
Good luck,
Bob