As I recall, the existing connector had three small screws that secured it to the deck. I unscrewed it and pulled it up to expose the wires below. I cut the wires, thus removing the connector completely. Then I drilled down thru the deck and the liner. Your suggestion might also work, but you would destroy the insulating rubber and the brass female receptacles inside the connector, so you would have to replace the connector anyway.
Whether you use the existing site or a new site, you will probably want to drill a small hole for the wires, ream out the plywood that is sandwiched between the deck and the liner, fill the hole with epoxy and then after it has cured, drill the hole for the wires again. This will help protect the wood below the deck from moisture.
After all that, and you have run your new wires up from below, connect the wires to the female connector, anchor the connector with the bedding compound (such as 3M 5200 or 4200 for a permanent solution or a different caulk for a mounting that you can more easily remove in the future), and screw it in place with the mounting screws.
Sailing isn't a matter of life and death. It's much more important than that!