Does one need to wash his hands after shaving, as one does after a haircut?
A shave is generally considered as a haircut for all intents and purposes, and we therefore find that the Rivevos Efraim (4:5, citing from Rav Baruch Yitzchak Levine, and from Rav Pesach Eliyahu Falk) rules that netilas yadayim is required after shaving.
However, Shut Divrei Chachamim (1:8) cites from Rav Moshe Feinstein that there is no need for netilas yadayim after shaving. The reason appears to be that the idea of washing hands after a haircut is because a haircut is considered something “dirty” on account of the sweat on one’s scalp, a shave is certainly different in this regard to a haircut.
Therefore, there is room to be lenient in this matter.