What I would do is this:
at the end of the season, do some diagnostic work. Look down in the bilge in the area, right behind where the transducer is, if you can. Look to see if there is any area that is not glassed in properly. Most likely though, you will not be able to see the back side of the transom where your transducer is because that area is probably filled with foam and under the rear deck.
So, what I'd do is this:
remove the tranducer screws
let the water (if any) run out
Try to dry the holes out, buy running a vaccum in reverse, with the air directed at the holes as long as you can. Let it dry out for a month at least and try to keep it out of the weather. After that, mix up some thinned epoxy (like CPES from
http://www.rotdoc.com) and inject it into the holes. This stuff is really potent so wear gloves, a fume respirator and goggles. Let it cure for 3-4 days. Then reinstall your transducer screws but use Boat Life Caulk to seal up the holes. The right way to do this is to caulk the holes and then put the screws in, but do not fully tighten them. Let the caulk cure for a day or so, then tighten them fully, that keeps the sealant in the hole and avoids it getting squeezed out. After that you should be OK. That is what most shops would do with the water out of the transom holes problem.