Nadeshiko

That'd be hilarious.
Do you think by any chance Nadeshiko would cut his hair?

I really don't think so. Then it might confuse some of the readers who are... less fast at catching up with stuff. I don't think they normally do that in mangas (?), but I"m not really sure. Either way I don't think so. PEACH-PIT might want to leave in some qualities of Nagihiko that could help prove that he's Nadeshiko later on (like pulling up the hair into a ponytail and speaking with a girly voice) and cutting it would cause Amu to be more skeptical ^^