Every cat and dog hand puppet I make naturally requires whiskers. The standard option is to use sewing thread, or buy some kind of string. I like making all elements of the puppet by hand, so I chose to create whiskers using the same materials as the rest of the puppet. I wasn't sure at first how to do this - not at all! But as with all art, there are synchronous occurrences and the light bulb goes on! I randomly turned on a video on Youtube about how to make a hood which included a thick cord to cinch it tight around the face. The lady created this cord in a way I would not have thought of myself, because in principle it involves laying out fibers horizontally, rather than vertically. Anyway, I took the technique and simply scaled it down to make thinner strings.
Check out this time-lapse video and then try it yourself!
All that's required is a little wool, water, soap and time. The amount of wool and the amount of pulling affect the thickness of your finished string. If your string is too thin, it will break, and if too thick, it won't look right as whiskers. Trial and error is necessary to obtain the right thickness and consistency for your project.