If you're thinking of replacing the 3.5mm connector - don't bother trying to do it nicely, just cut it off. The plastic surrounding the actual metal connector is cast around the metal. Real patient work with a small sharp knife might save you 1.5" of wire but cost you a fair bit of time and frustration...

I'd get some appropriate wire to run between the new to be RCA connectors and the end of the existing wire (it doesn't separate into part suitable for splitting and running to the RCA connectors. Cover each individual connection (Left, Right, and the 1->2 grounds) with small shrink tube, then cover the entire connection area with another piece of (somewhat larger) shrink tubing.

/Michael