Get a new wife ...........
Seriously ........ I would epoxy a piece of starboard to the stern and screw the transducer bracket into it. If you epoxy the bracket right to the stern, it is essentially there for the life of the boat and that becomes a problem when you change your depthfinder periodically. By screwing it into the starboard, you can change and remove the transducer bracket anytime and you haven't drilled holes in the boat.