In reply to MeMeMe:
2mm, that is fiddly!
Does it need to be that thin or would a fatter cable or bundle fit? Farnell do a 5.5mm OD 10way screened cable by the meter. Part no. 1619703
If it's not currently screened you could get the slightly thinner 8way version and use the screen as an extra core. Not really sure where you'd get much thinner than this off a reel (as opposed to by the whole reel)
RS do one at 3.9mm OD but you'd be looking at ~£55 for a whole reel.
I'd Hack up a cheap set of PTT mic+earbud phone headphones, use 2 runs. You'll need a good lens, scalpel and tweezers to find the cores but they're colour lacquered so when you find them you know which is which.
jk
Post edited at 14:52