Why did Wraith disguise herself as a man?
No particular reason is ever given for why Wraith chooses any particular disguise throughout the anime series or novels. Her M.O. involves cycling through an entire range of different disguises, male or female. The overriding purpose is that she blends into whichever environment she is seeking to infiltrate. That, and to ensure her true identity is as concealed as possible: in that case, pretending to be a man is doubly useful, in that it makes her less likely to be identified as the notorious (female) Wraith.