With the tape edges turned to rub against the pipe, the tapes curve cant slice most sizes of wire, even lightweight 2 wire communication wire is safe. I wouldn't worry until I was under16 gauge, unsheathed single strand, or smaller.
Small thinner tapes at 1/4 & ⅜ wide work best if you find yourself in a pinch. i would flatten the tape's stay tab by vice so there was to poking with a broken blade either.
I didn't learn the trick from an old and well known plumber