Is it permissible for the one who intends to do Hajj to remove anything from his nails or hair, knowing that he is going to offer an udhiyah and that this year he delegated one of his sons to slaughter the udhiyah?

Praise
be to Allah.

Firstly: 

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. 

Please see the answers to questions no.
7092 and 33743 

Secondly: 

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 replied: 

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.