I think that old wire goes down into the bilge, then across and back up the other side. Take a look under the dash and see if you can tell which way the wire goes as it leaves the actual remote. Or, could it be the wire goes from the electrical panel and then behind the cabin panels and then behind the head?
I don't have the parts manual (has wiring diagrams in it) with me, right now. Maybe it'll give the wiring route for that.
Regardless, I guess the important thing is how to get the new one over to the helm. I haven't done it myself, so hopefully someone that actually has will chime in. But, if I were to do it, I'd probably try and go down through the bilge area.
Underneath the sink, there is a false wall against the hull side. There's actually about 6" or 8" between the wall and the false wall. The box under the sink and the walls all are simply screwed in. You just have to look and feel as the screw heads get hidden in the carpeting. Once you remove the aft wall, you'll easily be able to access all of those wires that come up from the bilge - from the forward-most, starboard side of the bilge.
Next would be to remove the cubby by the driver's right knee.
Just an FYI, when I re-installed the walls (under the sink), I left the sink box off and pushed that stbd side wall (the false one) all the way back as far as I could. Just gave me a little more clearance to keep our cooler under there, along with some odds and ends.
I hope this helps at least a little bit and doesn't confuse the matter even more!