Men imitating women is strictly forbidden in Islam (as is women imitating men):
حَدَّثَنَا مُعَاذُ بْنُ فَضَالَةَ، حَدَّثَنَا هِشَامٌ، عَنْ يَحْيَى، عَنْ عِكْرِمَةَ، عَنِ ابْنِ عَبَّاسٍ، قَالَ لَعَنَ النَّبِيُّ صلى الله عليه وسلم الْمُخَنَّثِينَ مِنَ الرِّجَالِ، وَالْمُتَرَجِّلاَتِ مِنَ النِّسَاءِ وَقَالَ " أَخْرِجُوهُمْ مِنْ بُيُوتِكُمْ ". قَالَ فَأَخْرَجَ النَّبِيُّ صلى الله عليه وسلم فُلاَنًا، وَأَخْرَجَ عُمَرُ فُلاَنًا.
Narrated Ibn 'Abbas: The Prophet (ﷺ) cursed effeminate men (those men who are in the similitude (assume the manners of women) and those women who assume the manners of men, and he said, "Turn them out of your houses." The Prophet (ﷺ) turned out such-and-such man, and 'Umar turned out such-and-such woman.
— Sahih al-Bukhari, Book 77, Hadith 103
Wearing clothes of the opposite gender is considered imitation, and has been explicitly forbidden by the Prophet ﷺ with the strongest of warnings that whoever does so will be cursed by Allah:
حَدَّثَنَا زُهَيْرُ بْنُ حَرْبٍ، حَدَّثَنَا أَبُو عَامِرٍ، عَنْ سُلَيْمَانَ بْنِ بِلاَلٍ، عَنْ سُهَيْلٍ، عَنْ أَبِيهِ، عَنْ أَبِي هُرَيْرَةَ، قَالَ لَعَنَ رَسُولُ اللَّهِ صلى الله عليه وسلم الرَّجُلَ يَلْبَسُ لِبْسَةَ الْمَرْأَةِ وَالْمَرْأَةَ تَلْبَسُ لِبْسَةَ الرَّجُلِ.
Narrated AbuHurayrah: The Messenger of Allah (ﷺ) cursed the man who dressed like a woman and the woman who dressed like a man.
— Sunan Abi Dawud, Book 34, Hadith 79
Cross-dressing is strictly forbidden in Islam, regardless of the cause.