The best thing you can do to mount the transducers is to mount pieces of starboard (or other plastic "wood") to the transom and then mount the transducers to those. The starboard will allow you to adjust the transducers or put a new one on in the future without drilling new (additional) holes in the transom.
As for how to mount the starboard, there's a number of threads on that but in brief, cut the starboard to size and drill mounting holes in it. Do a test mount of the starboard and mark where the mounting holes meet the transom. Slightly over drill the holes into the transom. You only need to go through the outer layer of glass and part way into the core. If your transom is in good shape, the core should be clean and dry. If it's not or if water runs out when you drill that first hole, re-post here.
Assuming the core is good, use a dremel tool to under cut the core - e.g. you want to remove the core between the two layers of fiberglass. You can do this with a small grinding stone or even a bent nail mounted in a dremel or drill. I've usually drilled about a 1/2" hole and then I use a half in diameter grinding bit in a dremel tool. That lets me remove almost 1/4" of core under the glass. Make sure the holes are deep enough to accomodate the screw you plan on using. Clean everything up with a little alcohol or other solven and fill the holes with thickened epoxy. Then put the board up and re-drill holes that are appropriate for the screws you will use. I also like to undercut the starboard on the back side where the screws go through. Then when I attach the board, I can fill that undercut void with 3M4200 or silkaflex and it creates a little o-ring around the screw. This probably isn't necessary with the thickened epoxy behind it, but it doesn't hurt anything.
