My gut sense is that the thinner the wire (i.e., the greater the series resistance it provides), the greater the impact of any cable capacitance it might have. Sometimes that matters and sometimes it doesn't.
In general, earplug wire is pretty crappy. What I'd recommend more than that is the cable that usually accompanies CD-to-Soundcard connectors. It often has two conductors and a shield, and what strikes me as much sturdier insulation than what is found on the kind of earphones that break down easily. Even better, if you are making your own board, you can even use headers to simply plug the pot into the board and unplug when and if you want to remove the board, using the connectors at each end of the cable.
Steve Daniels at Small Bear recently sent me some spools of "pre-bonded" wire, and I have to say I've been very impressed with it. An absolute breeze to solder, strip, turn corners, twist together, and all those other things you need wire to do in a small chassis. Until recently I had been using some very nice 22awg stranded wire but the insulation is so bloody thick that the short lengths going to pots seem to actually be stressing the solder lugs (remember, shorter = stiffer). Good wire but a pain in the neck in some ways.