Is a woman allowed to shave her legs (not when it’s required for a tevilah) on Rosh Chodesh?
Yes. This not a major melachah, and there is no reason to think that it is prohibited.
Note that the general custom of not cutting fingernails or getting a haircut on Rosh Chodesh is mentioned in the Be’er Heitev (Orach Chayim 260:2), based on R’ Yehudah Ha-Chassid.
The Aruch HaShulchan (Orach Chayim 260:6) comments that since the custom has no basis in halacha (see Shulchan Aruch Ha-Rav, Orach Chayim 260), there is no special reason to adopt the custom (see Shach, Yoreh Deah 214:1; Dagul Merevava Yoreh Deah 214, concerning hataras nedarim).
Shaving legs will not be included in this matter, either.