When measuring LF 'signals' like a DC reference, the type of cabling from the DUT to the meter is more important than the actual contact and grounding to the DUT. At frequencies above a MHz, e.g. an oscilloscope probe, getting a proper wideband ground connection and HF signal 'launch' is probably more important, but below a couple of kHz, none of this matters.
Shielded twisted pair cables can essentially place an enclosure around the probe leads, all the way to the meter input jacks, and hopefully also remove a bunch of interference. By using a dedicated conductor (one conductor of the twisted pair) for 'ground' from the DUT, as well as an overall shield, more interference can be rejected. The standard procedure is to ground the shield at only one end of the cable, usually the measuring instrument side, so that it behaves as a pure electrostatic shield. At the DUT end, the twisted pair is used for signal + and 'ground' connections, just as in a normal probe.
In the audio world, star quad cable is used as an improvement over standard shielded twisted pair cable. Star quad uses two conductors for each of the conductors in a twisted pair, and because of the mechanical symmetry of such an arrangement, star quad is able to reject about 20dB or more of random EMI compared to a similarly shielded twisted pair. An overall shield will reduce electrostatic interference, as in the case of a coaxial cable, but unless a twisted pair (or quad) is used, there will be no rejection of current induced interference. The advantage of a star quad cable is that the twisted pair geometry is more precise, has more effective 'turns per inch', and thus rejects EMI better.
A good plan would thus be to use a twisted pair (or quad) connected with one conductor to the V+, one conductor to the V-, and the shield cut at the DUT end and connected only to the guard, chassis, or V- connection as appropriate to your meter or test instrument. Mogami 2799 is a nice miniature star quad cable that is very small but still not a huge pain to terminate. If your connectors can handle larger diameter cable, Mogami 2534 is a better cable - it has less capacitance, and because of its larger overall size, you get more copper and better dimensional stability. I have some 2534 cables that are 30 years old and they still work beautifully despite being flexed and used without great care. Conventional shielded twisted pair cables can work well, probably better than coax, but if their construction uses a drain wire, the mechanical displacement of the drain wire against the real twisted pair will mess up the symmetry of the twisted pair, and thus it will not reject as much EMI as possible.