It is permissible for the pilgrim performing Umrah to shorten his hair and he does not have to shave it. It is recommended for him to shave his hair or shorten it at Al-Marwah
حَدَّثَنِي حَامِدُ بْنُ عُمَرَ الْبَكْرَاوِيُّ، حَدَّثَنَا عَبْدُ الْوَاحِدِ، عَنْ عَاصِمٍ، عَنْ أَبِي نَضْرَةَ، قَالَ كُنْتُ عِنْدَ جَابِرِ بْنِ عَبْدِ اللَّهِ فَأَتَاهُ آتٍ فَقَالَ إِنَّ ابْنَ عَبَّاسٍ وَابْنَ الزُّبَيْرِ اخْتَلَفَا فِي الْمُتْعَتَيْنِ فَقَالَ جَابِرٌ فَعَلْنَاهُمَا مَعَ رَسُولِ اللَّهِ صلى الله عليه وسلم ثُمَّ نَهَانَا عَنْهُمَا عُمَرُ فَلَمْ نَعُدْ لَهُمَا .
Abd Nadra reported: While I was in the company of Jibir, a person came and said: There is difference of opinion amomg Ibn Abbas and Ibn Zubair about two Mut'as (benefits, Tamattul in Hajj and temporary marriage with women), whereupon jibir said: We have been doing this during the lifetime of Allah's Messenger (way peace be upon him), and then 'Umar forbade us to do so, and we never resorted to them.