Yes, that is permissible. We have already said in the answer to Question no. 36567 that it is haraam for the one who is going to offer the sacrifice to remove anything from his hair, nails or skin. But this ruling applies only to the one who is going to offer the sacrifice, namely the owner of the sacrificial animal. 

Shaykh Ibn Baaz (may Allaah have mercy on him) said: 

With regard to the family of the one who is going to offer the sacrifice, they are not subject to any obligations, and it is not forbidden for them to remove anything from their hair or nails, according to the sounder of the two scholarly views. Rather the ruling applies only to the one who is going to offer the sacrifice, the one who has bought the sacrificial animal from his own wealth. Fataawa Islamiyyah, 2/316. 

It says in Fataawa al-Lajnah al-Daa’imah (11/397): 

It is prescribed for the one who wants to offer a sacrifice, once the new moon of Dhu’l-Hijjah appears, not to remove anything from his hair, nails or skin, until he has offered the sacrifice, because of the report narrated by the group except al-Bukhaari, from Umm Salamah (may Allaah be pleased with her), that the Messenger of Allaah (peace and blessings of Allaah be upon him) said: “When you see the new moon of Dhu’l-Hijjah, if any one of you wants to offer a sacrifice, let him leave his hair and nails alone.” A version narrated by Abu Dawood (2791) and Muslim (1977) says: “Whoever has an animal to slaughter, when the new moon of Dhu’l-Hijjah appears, let him not remove anything from his hair or nails until he has offered the sacrifice.” This applies whether he is going to slaughter the sacrifice himself or he has appointed someone else to do it; but with regard to those on whose behalf the sacrifice is being offered [i.e., his family etc], that is not prescribed for them, because there is no report to that effect. 

Shaykh Ibn ‘Uthaymeen said in al-Sharh al-Mumti’ (7/530): 

For the person on whose behalf the sacrifice is offered, there is no blame on him if he removes anything from his hair or nails. The evidence for that is as follows: 

1 – This is the apparent meaning of the hadeeth, which indicates that the prohibition applies only to the one who is going to offer the sacrifice. Based on this, the prohibition applies only to the head of the household, not to the members of his family, because the Prophet (peace and blessings of Allaah be upon him) connected the ruling to the one who is going to offer the sacrifice, so what is understood is that this ruling does not apply to those on whose behalf the sacrifice is offered. 

2 – The Prophet (peace and blessings of Allaah be upon him) used to offer the sacrifice on behalf of his household and it is not narrated that he said to them, “Do not remove anything from your hair or nails or skin.” If that had been forbidden for them, the Prophet (peace and blessings of Allaah be upon him) would have told them not to do it. This view is the more correct opinion.