Grind a large area around where your transducer is going, say 12" diameter or so. Use a 4" hole saw from the inside of your vessel, cut down through your interior laminate and slowly through your core material, pop out the offensive matter, cut a bunch of circles from fiberglass mat and structure material, like an 1808. Scrape the bottom of your hole with a putty knife/screwdriver/old chisel/etc, put some tape on the outside of your hull to keep the resin in place (2" blue 3M works pretty good for this), hot coat your area well so that the balsa/foam/whatever absorbs as much as possible. On a piece of card board put some resin down with a chip brush and start stacking layers of fiberglass, you should start with 2-3 layers of mat, wet those out and put them in the hole, work the air out of the laminate and continue alternanting between layers of structure and mat, say 4-5 layers of structure then a mat making sure to remove the air as you go. Depending on how thick your core material is you may want to consider using slightly less catalyst than you would normally, so that the laminate doesn't exotherm and create a bunch of heat which will crystalize your resin and make it a poor bond. I would suggest working with polyester resin. When you get to the surface of your interior laminate put a larger area of fiberglass down, say a 6" circle of structure material mat side down and then an 8" circle of structure material mat side down with 2 layers of resin rich mat which you've feathered the edge on so that the edge extends past your 8" layer of structure - this will give you a nice working surface which bonds well and needs little if any fairing, just some gelcoat when it's done curing. You can now drill and compress to your hearts desire (right up until you distort the nut or break the hollow transducer shaft) without crushing any core material.
If working with epoxy (shakes head) you will need to revisit your project and go in only a few layers at a time so you don't exotherm.