The easiest thing to do is to just replace the speaker wiring entirely - well, maybe not the easiest, but the best, I would say.
You can abandon the existing speaker wiring in place, just leave it disconnected, and run all new wire to your speakers. If you are running amps in the trunk, you'll need to run RCA cables back there from the head unit. Otherwise, you'll just need to run new speaker wire from the head unit to each of the speaker locations. Don't run any speaker wire along the passenger side sill, that is where the battery cable is so you'll pick up some noise if you do.
Fish your new wire from behind the head unit across the steering column area, and down the driver's door sill - there is a nice cavity there that has factory wire running in it that provides plenty of room for speaker wire.
As far as the connector for the head unit, is it not already hooked up? I'm not sure I understand why you would need a new connector there.