See this M.Y. question related to the order for cutting one's nails.
Does one need to follow this same order when one files or paints (manicures) the nails, or does it only apply to cutting?
The SHulchan Aruch that discusses the concept of having an order for cutting nails is written with regard to cutting nails for Shabbat and Yom Tov. I understand that this is related to beautifying one's body / appearance. If that's so, then filing / manicuring one's nails seems to fall in the same category / reasoning.