Assalamoalaikum. Shall I wait not to cut hairs and nails if my relative will slaughter on my behalf in my country where Eid ul Azha will be celebrated after 1 or 2 days than the place where I leave?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.

As long as you are going to offer an animal sacrifice, you should not remove any of your hair or nails or skin until your sacrifice is slaughtered in your country even if they slaughter it on the second or third day after the ‘Eed. This is because of the all-inclusiveness of the words of the Prophet, sallallaahu ‘alayhi wa sallam: "When the ten days (of Thul-Hijjah) begin, and one of you intends to offer an animal sacrifice, he shall not remove any part of his hair or skin." [Muslim and Ibn Maajah] Al-Mardaawi  said: "This prohibition ends once the person offers the animal sacrifice." [Al-Insaaf]

For more benefit, please, refer to Fataaw, 102350 and 89597.

Ibn ‘Uthaymeen said about offering sacrifice in the country where the person resides instead of sending it to another country: "If it is sacrificed in another country, one does not know when it is sacrificed. It could be sacrificed before the (prescribed) time out of ignorance on part of the one sacrificing, and it could be sacrificed after it. Thereafter, one is bound by it, because one does not remove any part of his hair, skin or nails whatsoever until after he sacrifices, but he does not know when this sacrificial animal is slaughtered; so he remains suspended all the days of ‘Eed not removing any of his hair, nails or skin at all, because he does not know whether or not the sacrificial animal was slaughtered, especially if the country where the sacrifice is to be offered is in the east where they often delay it for one day or perhaps two. In this case, he would remain uncertain from the day of 'Eed throughout the three days of Tashreeq (11, 12, and 13 Thul-Hijjah), and perhaps until the fourteenth or fifteenth day of Thul-Hijjah."

On the other hand, some scholars were less stringent on the matter, suggesting that it is enough to verify that the time prescribed for offering the animal sacrifice begins in the country of the person who has authorized another person to sacrifice. From then on, it is permissible for the authorizer to remove his hair or nails.

Ibn Jibreen was asked, "When is the person offering an animal sacrifice allowed to cut his hair or nails, given that his animal sacrifice may be slaughtered a day before or after depending on the country where it is slaughtered?"

He replied, “When the time for slaughtering sets in in the country of the one donating (the sacrifice), it is permissible for him to remove the hair and nails, even if he does not verify the slaughtering of his sacrificial animal on that day, just as a Muhrim (the pilgrim who is assuming Ihraam) removes Ihraam when he casts (the pebbles) and shaves, even if it is before the slaughtering of his sacrificial animal in his country."

Anyway, one should wait until he is certain that his animal sacrifice has been slaughtered (before removing any hair, nails, or skin) for his liability to be clear with certainty. This is based on the view that it is prohibited for the person who is going to offer an animal sacrifice to remove any of his hair or nails.

As for the view that it is only disliked, then the matter is less stringent. For further information, please, refer to Fatwa 83881.

Allaah Knows best.