I just shot video of this the other day.

Most people use scissors, but I don't cut into hairline with anything but a blade.

Basically, what I do is I grip the base with two fingers on one side and two fingers on the other side of the cut (with the same hand).

I make absolutely sure that none of the hairs that are on the cut line are trapped between my fingers and the base. There needs to be ZERO tension on any of the hairs near the cut. It might take a few tries to get your hand situated, but once you are in place all you have to do is stretch the base between the two sets of fingers and use the tip of a triangular x-acto blade to slowly cut your way through the lace. You will feel and hear a little "tick, tick" as the lace is cut.

If you do this with ZERO TENSION on the hairs, you will have no stubble.

The lace can be a bit stretchy, but once you get the hang of it this is by far the easiest way to cut into hairline without sacrificing hair.

I like your tape idea, BTW