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 Sahih Muslim 1248
Arabic hadith text
وَحَدَّثَنَا حَجَّاجُ بْنُ الشَّاعِرِ، حَدَّثَنَا مُعَلَّى بْنُ أَسَدٍ، حَدَّثَنَا وُهَيْبُ بْنُ خَالِدٍ، عَنْ دَاوُدَ، عَنْ أَبِي نَضْرَةَ، عَنْ جَابِرٍ، وَعَنْ أَبِي سَعِيدٍ الْخُدْرِيِّ، - رضى الله عنهما - قَالاَقَدِمْنَا مَعَ النَّبِيِّ صلى الله عليه وسلم وَنَحْنُ نَصْرُخُ بِالْحَجِّ صُرَاخًا .
Translation
jibir and Abil Salld al-Khudri (Allah be pleased with them) reported
We went with Allah's Apostle (ﷺ) and we were pronouncing Talbiya for Hajj loudly.