Is it permissible to do electrolysis on eyebrows on rosh chodesh?
The reason for not taking haircuts or cutting nails on Rosh Chodesh is from the “Tzavah (will) of R’ Yehudah Hachasid”. There are different opinions if this tzavah was meant for his descendents or for everyone. The custom of many is to be careful about it.
If one has the minhag to be careful about it, then this would seem to be included in cutting hair. However if the hair or nails are being cut for a mitzvah reason, (chatzitza for mikvah, washing hands, or long nails when baking matzos for Pesach) it is permitted.
M:A O:C 260, Nodeh B’yihudah E:H 79, Chasam Sofer Y:D 138, Mili d’chasidusa brought in shmiras Haguf V’hanefesh 68-10, Ben Ish Chai 2-21, Likras Shabbos 6 ftnt 16.