Praise be to Allah.
It is not permissible for the one who is going to offer an udhiyah to remove anything from his hair or skin after the first ten days of Dhu’l-Hijjah begin, because the Prophet (blessings and peace of Allah be upon him) said: “When the ten (days of Dhu’l-Hijjah) begin, and one of you wants to offer a sacrifice, let nothing touch his hair or skin.”
Narrated by Muslim (1977)
This ruling applies specifically to the one who is offering the udhiyah; as for the one whom he appoints to buy it, slaughter it or distribute the meat on his behalf, he is not included in this ruling.
If a person does Hajj and also wants to offer an udhiyah or to appoint someone to offer the udhiyah on his behalf in his own country, he may remove some of his hair at the time of exiting ihram following his ‘umrah or Hajj, because removing some of the hair at the time of exiting ihram is one of the rituals.
Shaykh Ibn Baaz (may Allah have mercy on him) was asked:
There is a man who is intending to do Hajj and he intends to do tamattu‘ (‘Umrah followed by Hajj, exiting ihram in between); he has also left instructions for the udhiyah to be done. What is the ruling if he wants to exit from his ihram following the rituals of ‘umrah?
He has to shave his head or cut his hair, regardless of whether he is appointed to offer the udhiyah on behalf of someone else or is offering it on his own behalf. He must do that if he is doing tamattu‘, after completing his ‘umrah, before doing any of the things that are prohibited whilst in ihram. End quote from Majmoo‘ al-Fataawa (17/233)
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: When the pilgrim has done ‘Umrah, he must cut his hair, even if he wants to offer an udhiyah in his own country, because cutting the hair following ‘Umrah is one of the rituals.
End quote from Majmoo‘ al-Fataawa (25/141)
And Allah knows best.