Having used this term as a punchline to a joke in the politically incorrect medium of a tattoo parlour, I was surprised at the response of one of the artists, who put down his buzzing tattoo machine and addressed the term at hand.
"You do know that it's an actual measurement in machining?"
Given this bloke's penchant for the leg-pull, I smiled, and the guy tattooing my arm took the opportunity to pause himself and stretch, stiff as he was from holding the unnatural position.
"Back when I was a machinist, a "cunt hair" was 1/64", which if you think about it, is actually thinner than a human hair. But it was typically added to machinist instructions, or the foreman coming by saying "bump it 2 CH" or something on a diagram so that nobody could object to it in writing.
I looked at him quite carefully to see the telltale twinkle in his eye indicating that it was actually a gigantic wind-up, but it never came. Instead, quite the letdown, he brought the tattoo machine back into position and resumed the calf tattoo he was applying.