Cable wires - confirmation of live and ground
Cables don't care which way around you use them. The only difference between a live wire and a ground wire is that one of them is connected to live, and one of them is connected to ground. The electricity doesn't care what colour of wire it's flowing through.

Feel free to use green and yellow wires for 240V.  But don't actually do that because the next electrician who sees the cable might electrocute themselves by mistake! For mains electricity, colour codes are there so that people don't electrocute themselves or blow things up by mistake.

Since this is not mains electricity, and you are dealing with only a few volts (nowhere near 120 or 240V) and there is no risk of electrocution, and probably nobody will see it except you, you can use whichever wire you want for whatever purpose you want.

If you are going to have a ground wire, I would suggest using the outer wire for ground. That way, in case the black insulation gets damaged and the wire touches something metal through a hole in the insulation, it has less chance of damaging your circuit. Otherwise, it doesn't matter.



Edit: I missed that your cable already has a connector on one end. In that case, the connector is wired a certain way around. When your multimeter shows a positive voltage, the red lead is touching the positive wire, so in this case, the inner one is positive.