Are there halachic concerns with using wax to remove a mustache off of someone's lip?
Does it make a difference if it is for aesthetic appeal or some other reason?
Could this be considered chukat goyim?
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Waxing to shave is permitted in general, see e.g., here from R Zev Farber
According to the halacha [...] it is forbidden for a man to shave off the hair of his temples or to shave off the corners of his beard. Both of these rules apply only to shaving with a razor. Using a depilating cream, a waxing process, or just pulling the hair out by hand would not be forbidden. Trimming with scissors and most forms of electric shavers (where the razor does not touch the face) are not forbidden either.
In general, doing something that other Jews do is not chukat goyim (see here on MY).
There is no issue of lo yilbash gever simlat isha (to act in the way of women) either because this applies to beautifying oneself in the way of women or wearing women garments.
I checked the above with R Binyamin Tabady who concurs that waxing to remove a mustache is permitted.