The tip and ring of the rca connector at one end of the cable must both be connected to the tip and ring, respectively of the rca connector at the other end of the cable. Your initial post indicated that the canare cable you're using has one wire in the center and a insulating wire mesh surrounding the center wire. The links you provided all discuss building cables with multiple center wires and use one of (or a pair of) the central wires to connect the rca's rings and a different central wire to connect the rca's tips.
Thus, in the cables contemplated in the links, the insulating wire mesh is not needed to complete the connection between the rcas' ring connectors and can be soldiered onto only one of the rings to help isolate the central cables from interference, etc.
In your example, with only one central wire, the insulating wire mesh IS needed to connect the rca connectors rings and complete the circuit. Thus, it should be soldiered onto both rca rings (outer connectors)
in order to create a complete circuit.