Praise be to Allah.
If that is indeed the case, then it is permissible for them to cut their hair short, but only as short as is necessary, and they are not permitted to cut their hair short to look like kaafir women, because the Prophet (peace and blessings of Allah be upon him) said, “Whoever imitates a people is one of them.”
(Fatawa al-Lajnah al-Daa’imah, 5/182).
Similarly, they are not permitted to cut their hair short in ways that resemble men’s hairstyles, because of the hadith of Ibn ‘Abbaas (may Allah be pleased with them both) who said: “The Messenger of Allah (peace and blessings of Allah be upon him) cursed men who imitate women and women who imitate men.” (Reported by al-Bukhari, 5435).
And Allah knows best.