Question: Is it appropriate to shave before shacharis?
Answer: The Mishna (Shabbos 9b) writes that one mustn’t cut one’s hair before davening mincha as we are concerned that they will forget to daven.
The Shulchan Aruch (OC 89:7) writes that this prohibition does not extend to before shacharis as it isn’t common for people to have a haircut so early in the morning (See Rambam, Tefilla 6:7).
Nonetheless, the Elya Rabba (89:12) explains that this refers to the time before alos hashachar. All work, including haircuts, is forbidden after that time before one davens. Thus, the Mishna Berura (89:36) writes that one can’t have a haircut after alos hashachar before shacharis. He concedes, however, that it is sufficient to just say the birchos hashachar first for activities that one regularly gets up early to perform.
R’ Shlomo Zalman Auerbach (Halichos Shlomo, Tefilla 2:7) writes that one shouldn’t shave before shacharis as it is no different from taking a haircut (See Ohr Letzion 2:7:9).
However, the Piskei Teshuvos (89:24) writes that people who shave regularly may do so before shacharis as we don’t need to be worried that they will get distracted and miss davening. Similarly, R’ David Yosef (Halacha Berura 89:36) allows it, writing that there’s a difference between having a haircut and shaving, etc. (See Rivevos Ephraim 1:66).In conclusion, while it is preferable to shave at other times, one who shaves regularly may do so before shacharis. Ideally, one should say birchos hashachar beforehand.