5200 cures by moisture absorption, it would be very slow to cure in there (unless the core is wet!!), and it is very flexible compared to the other materials involved, and does not flow well. I would leave it alone rather than do that. If it is only delaminated on one side (more on this in a minute) then I would drill a couple of holes at the bottom, and a couple at the top of the area, then pump West Six10 in from the BOTTOM until you see it coming out the top holes. The holes only need to be about 5/16. Plug the ones that it comes out of first and keep going until you get some out of all of them. You may be able to tape them over to plug them, but more likely need some extra hands to stick a finger over. It will not run out, but will get pushed out from the pressure of the caulking gun. When you are done fill the holes and strike it off with a squeegee, stick, or whatever.

The reasons for this are, you want to use something with good bonding capability that is as stiff as the Balsa core (which is pretty stiff as core materials go). You want to push it in from the bottom and let the air out the top - working from the top down will guarantee a bunch of voids. West Six10 is expensive, but comes in a caulking tube which makes it easy to pump into tight spaces, flows reasonably easy but is thick enough it will not flow back out on its own. It also has a pretty slow cure time, giving you a couple of hours to work at 60 deg temperatures. Cut the end of the supplied mixing nozzle as big as possible but small enough to still fit in the drilled holes. These holes will be below the waterline? I would then grind a small recess over the holes, put a piece or two of 17 oz type biax or triax cloth, fair and paint. I do not trust thickened epoxy by itself to fill a hole below the waterline, too easy to knock loose from the skin. The consequences of even a tiny leak below the waterline in a balsa cored boat are not at all pretty.

Blasa core is stiff enough that if an area is depressed enough to delaminate the outside, it often delaminates the inside, particularly around the periphery of the area depressed. You may want to check both inside and outside by tapping. I find that the edge of a quarter coin works better than almost anything else for this purpose. In your case it sounds like it was just pressed in slowly over time, which might just compress the balsa. In impact type damage there is much greater chance of inside skin delamination.