If he's shaving with an electric shaver, then, according to the Poskim that consider electric shavers to be Misparayim k'Ein Ta'ar, there shouldn't be a problem with him using the shaver anywhere except Beis ha'Shechi and Beis ha'Ervah (see Shulchan Aruch YD 182:1) - regardless of what men do. If he's shaving with a razor then it depends on the what is common behavior for men. Everyone agrees that it is okay for the barber to finish off a haircut by shaving the back of the neck with a razor. That is normal for men. If it is normal now for men to shave their chests, then it shouldn't be considered Tikunei Nashim. (See the Prishah that says that the Minhag of the non-Jews in this case can be used to determine the permissibility of shaving a certain area). If men don't shave their chests it should be a problem, even though women don't. Shaving off body hair, in general, has traditionally been a women's activity, and if they don't shave there it's only because they don't need to. There are Poskim that go so far as to say that shaving off one's beard is a violation of Lo Yilbash (Tzemech Tzedek, #93) even though women don't have facial hair to shave.

Regarding shortening underarm hair: the wording of the Gemara (Nazir 58b) is "ha'Ma'avir Beis ha'Shechi..." which implies that the prohibition is to completely remove the hair there and not simply to trim it. Furthermore, Rashi (59a, D.H. Ika d'Amri) explains that removing the underarm hair is included in Lo Yilbash because it is ugly and disgraceful (Nivul) for a woman to have hair there and therefore normal for them to remove it. Trimmed hair would certainly still be considered Nivul for a woman and therefore wouldn't be included in the Isur for men.

Kol Tuv,

Yonasan Sigler

This is not a Psak Halachah