I Can Sympathsize With Your Situation...........
........... as I am/was looking at a similar situation to yours. It's a bit of a conundrum which basically involved a leak at the deck-hull joint, but I won't bore you with the details. What I did want to mention is that playing with the rub rail is the bugger of all creation.
When the boat was delivered from the factory in 1998, it developed a leak under the chain plate in very short order. Re-sealing necessitated prying out a short section of the starboard rub rail and was it ever fun. The dealer and I went at it with three hair dryers and and a dozen oak wedges before we opened it up enough to get at the base of the chain plate. I notice that you refer to "screws" holding the joint together and I am taking this to mean wood screws. I notice when we had the rub rail pried out, the joint was fastened by 1/4" machine screws spaced about every four inches. All went very well and that was the end of that repair. Attached is a picture Hunter sent along showing the two piece construction of the rub rail.
Now fast forward fourteen years and another problem requiring the partial opening of the rub rail rears it's ugly head. However in this case, it looks like the whole starboard side of the boat may require removal of the rub rail. It's a very small leak which appears only when it rains but I have a strong aversion to leaks.
I recently talked to Eddie Breeden of Hunter Marine and we looked at what was involved with this job. Lots of heat to make older rub rail pliable plus they have a nasty habit of shrinking once they are released from the confines of the hull-deck joint hardware. He suggested the rub rail be held to length downstream of the
removal, using a large C-clamp. My fear was that the rub rail might be so rigid it would require replacement. And unfortunately, it's no longer made in that shape.
Another piece of information which is common to most boats, is the sealant in the deck-hull joint is 3M 5200. This will also be covering the the screws which means you may not be able to remove them to reseal.
Given the above information, I finally decided to leave the leak rather than deal with what may become a very large problem and the final result may be far worse than the initital small leak. Additionly, I chose not to seal the leak from the inside due to the worry of having the cavity fill with a small amount of water which
would eventually freeze in the winter and cause progressive expansion damage.