I would be tempted to remove the handles and seal them internally as you described, as you will probably find the external fixed sealant may come loose after a period of time
I do this to
all my handles just as a precaution. Always use black sealant if you can for obvious squeeze out reasons.
I just place a very thin beed of mastic along the inner edge of the ply before fixing in the handles. Its not enough to prevent removal of the handles but enough to give an airtight seal.
Penn have started making these corner handles with a very tight radius that
may be better for some people:-
Dave