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Here's another option that would still allow external attachment of your transducers. It might more of a hassle than it's worth, but I'll let you decide.
This would still require putting a couple of screws into the transom (see illustration) but with much less chance of water intrusion. One piece of HDPE is screwed to the boat; the screws and back side of the HDPE are covered in 5200. A second piece of HDPE is then screwed to the first, again after the screws and back face are covered in 5200. Then, transducers can be screwed into the layers of HDPE, and as long as the screws don't penetrate both layers, there is very little chance water will intrude.
If you use new cutting board and round off the edges of the outermost piece of HDPE with a router, it won't even look bad. Before I rebuilt my transom (when my boat was new to me, and I was scared to put holes in it), I did this and it worked well. After I rebuilt, I decided it was overkill and I just drilled into the transom, applied 5200 and screwed my 'ducer directly to the transom. If that worries you, though, this will work.