So the outside of the plug should be connected to the white cable, which in turn should be connected to the -V of the powersupply
so normally putting one probe on the outside (sleeve of the connector) and the other at the end of the white cable gives me a reading on resistance
putting one probe on the inside of the connector and the other at the end of the white cable gives no reading
?
If "no reading" is zero ohms, it's a short, in other words your "inside of the connector" is connected to the white wire. That's probably not what you want.
To test it touch the multimeter probes together, you should get 0 ohms (or very close to 0), that's what you are looking for in your wiring.
Some multimeters have continuity mode, which basically is a beeper/buzzer for exactly this purpose. Use that if you have it.