Q. Is a man allowed to remove or shave body hair for the purpose of helping to control body odor?
If so, is there a preferred method? Shinui?
If so, may it be done during the three weeks? The nine days?

A. On question 563 in regards for a man trimming his eyebrows if they are unruly and get into his eyes, or if his wife asking him to do it, we wrote; Shulchan Aruch (Y.D. 182: 1) rules that it is forbidden for a man to remove bodily hair growth that women usually remove such as hair of the armpits or the genital area, due to the “lo yilbash” or not dressing like a woman prohibition. However Mordechai (Shabbos 50: 327) permits in cases of great discomfort or pain. Avnei Yoshfe (Y.D. 91) accordingly permits trimming eyebrows, adding that women pluck those hairs and do not usually trim them. Nishmas Avrohom (Y.D. 182 p. 140) quoting Horav S.Z. Auerbach Zt”l that permits the removal of embarrassing excessive hair between the eyebrows, (unibrow). Similarly Levush Malchus (4: 13) permits trimming with scissors, but not plucking with pincers. (See also Chevel Nachalaso 13, Birchas Yehudah (Y.D. 9) and other Poskim quoted in their notes for comparable opinions. See also Bava Kama 117a, that Rebbi Yochanan had very long eyebrows that covered his eyes).
Horav Shlomo Miller’s Shlit”a opinion is that the eyebrows can be trimmed for the sake of one being able to see properly but not with the exactness and meticulousness typical in women’s facial treatment.
On question 1348 in regards to removing all hair from head as in “male pattern baldness,” in order to look cleaner or better using depilatory creams or similar, we wrote; Horav Shlomo Miller’s Shlit’a opinion is that there is no real heter or procedure to permit complete hair removal from head, including peyos. There are some biblical exceptions however, such as the metzorah on the day he is ritually cleansed (Vayikra 14: 8-9) and the nazir (BaMidbar 6:13,18) when the days of his consecration are fulfilled, in which all body hair was removed. However, doing it via drug ingestion, (if medically accepted) the Rov Shlit’a maintains that it probably would be permitted.
In regards to your particular question the same would apply. The Rov maintains that there are probably better common everyday methods to control body odor. Cutting hair short, without total removal is also a better option. Nonetheless, if removing all body hair besides the payos is recommended by doctors, it could be done when needed for medical reasons.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit’a