Why take it apart? You can just cut it mid line and splice directly to that. Chances are the failure point isn't right on the last bit of the headset end of the cable length.

IME it's either at the plug side, or at the headphone. I've never had a cable go bad in the middle. I think it's the same kind of issue as apple's power connectors: they always go bad next to the connectors.

I've had headphone cables break in the middle as the cable got hard and brittle from body heat / sweat over time.