Bill, you can drill through the stern no problem. Bass boats, (shudder), do it all the time with sensors, etc. Make sure it's above the water line a tad, and seal up the wire good, (I don't get into the sealant debates), and maybe put a small clam shell vent over it. It looks like you sail on a lake, so following seas shouldn't be a problem. But if you seal it, it won't matter.
Drill man..