Can a woman wear a new hat that was original designed for a man but was changed in such a way that a man would not wear it. For example if I were to buy a grey fedora and change the band for a Pink one. Would it be permited to wear?

Shalom u'verachah, The prohibition against one sex wearing the clothing of the other sex is due to the fact that one may disguise themselves and seclude themselves with a member of the opposite sex. When dealing with one item of clothing that is obviously not to be worn by a man, such as the hat that you spoke of, I do not see any problem. Kol Tuv