The way I do it...

Take a strip and fold it in half, end to end, then cut it in two across the fold. Hold one half on each side of the string and take an alligator clip or hemostat and clip both halves to the string. Clip onto them at one end or the other to leave the middle open. Then take serving thread and tie a series of overhand knots centered lengthwise, on top, then underneath, back on top, etc. until you've got about 10 knots, 5 per side. Pull each knot tight as you can get it. Then finish off with a square knot. Clip the tag ends of the thread about 1/8" long. Then melt the tag ends so they won't come undone.

Repeat for the other end of the string. Then seperate the strands.

I've also seen folks do the same thing except using a very small zip tie. Once you get the zip started, grab the end of the zip tie with pliers and pull it as tight as you can. Pull until you have to grit your teeth and that vein pops out on your forehead! Then clip off the excess. It's probably easier that way, but I never seem to have that size zips when I install cat whiskers.[&:]

Doing them that way, I've never yet had a set of whiskers slide around on the string, come apart or fall off. They last longer than the string does.