The aforesaid tradition has also been transmitted by Hisham n. Hassan through a different chain of narrators. This version adds:He said to the barber: Start with the right side and shave it.
حَدَّثَنَا عُبَيْدُ بْنُ هِشَامٍ أَبُو نُعَيْمٍ الْحَلَبِيُّ، وَعَمْرُو بْنُ عُثْمَانَ الْمَعْنَى، - قَالاَ - حَدَّثَنَا سُفْيَانُ، عَنْ هِشَامِ بْنِ حَسَّانَ، بِإِسْنَادِهِ بِهَذَا قَالَ فِيهِ قَالَ لِلْحَالِقِ " ابْدَأْ بِشِقِّي الأَيْمَنِ فَاحْلِقْهُ " .
AbuDaud
The Rites of Hajj (Kitab Al-Manasik Wa'l-Hajj) • Hadith 1982