It is permissible for the Muhrim to wash his body and head
وَحَدَّثَنَاهُ إِسْحَاقُ بْنُ إِبْرَاهِيمَ، وَعَلِيُّ بْنُ خَشْرَمٍ، قَالاَ أَخْبَرَنَا عِيسَى بْنُ يُونُسَ، حَدَّثَنَا ابْنُ جُرَيْجٍ، أَخْبَرَنِي زَيْدُ بْنُ أَسْلَمَ، بِهَذَا الإِسْنَادِ وَقَالَ فَأَمَرَّ أَبُو أَيُّوبَ بِيَدَيْهِ عَلَى رَأْسِهِ جَمِيعًا عَلَى جَمِيعِ رَأْسِهِ فَأَقْبَلَ بِهِمَا وَأَدْبَرَ فَقَالَ الْمِسْوَرُ لاِبْنِ عَبَّاسٍ لاَ أُمَارِيكَ أَبَدًا .
This hadith has been narrated on the authority of Zaid b. Aslam with the same chain of transmitters that Abu Ayyub rubbed his whole head with his hands and then moved them forward and backward. Miswar said to Ibn 'Abbas: I would never dispute with you (in future).