Maine Sail doesn't recommend his butyl tape for under water applications. The lower gudgeon goes under water in some conditions.
5200 will permanently adhere them. You don't want that, they need to be replaceable.
I used LifeCalk on my Catalina 25. Any polysulfide should be fine. 4200 should also work, I just prefer working with LifeCalk.
I don't know if this is true on the Catalina 22, but on the Catalina 25 the backing plate for the gudgeons is buried inside the transom. The best way to access it is to use a hole saw to add a big hole, then put a deck plate over it. This shows the process on the Catalina 25: How to replace upper gudgeon on Catalina 25
I to used lifecalk on my 85 catalina 25. as alex w said I had to cut a hole to grt to the upper grudon. what really surprised me was that there were no backing plates, just washers and a nut. I cut the angle off of the old grudon and used the plate as a backing. this way the holes for the bolts lined up perfectly.
My '74 C22 had no backing plate, just washers. I upgraded them to gigantic washers, 316 stainless fasteners, and nylock nuts.
I bedded the gudgeons with 4200, but I can't say I recommend it as they still leaked afterwards! Perhaps there is just too much movement and a heavy duty backing plate is needed.
One problem is that it's hard to get a rigid attachment because the bolts go through the hull and the liner, but there is nothing between the two- just open space. So the liner which is thin and flexible is supporting the tension on the bolts.
You should be able to access the gudgeon nuts through the port side cockpit locker.