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 1247
Arabic hadith text
حَدَّثَنِي عُبَيْدُ اللَّهِ بْنُ عُمَرَ الْقَوَارِيرِيُّ، حَدَّثَنَا عَبْدُ الأَعْلَى بْنُ عَبْدِ الأَعْلَى، حَدَّثَنَا دَاوُدُ، عَنْ أَبِي نَضْرَةَ، عَنْ أَبِي سَعِيدٍ، قَالَ خَرَجْنَا مَعَ رَسُولِ اللَّهِ صلى الله عليه وسلم نَصْرُخُ بِالْحَجِّ صُرَاخًا فَلَمَّا قَدِمْنَا مَكَّةَأَمَرَنَا أَنْ نَجْعَلَهَا عُمْرَةً إِلاَّ مَنْ سَاقَ الْهَدْىَ فَلَمَّا كَانَ يَوْمُ التَّرْوِيَةِ وَرُحْنَا إِلَى مِنًى أَهْلَلْنَا بِالْحَجِّ .
Translation
Abu Sa'id (Allah be pleased with him) reported
We went out with Allah's messenger (ﷺ) pronouncing loudly the Talbiya for Hajj When we came to Mecca, he commanded us that we should change this (Ihram for Hajj) to that of Umra except one who had brought the sacrificial animal with him. When it was the day of Tarwiya (8th of Dhul-Hijja) and we went to Mini, we (again) pronounced Talbiya for Hajj.