Bukhari

Hadith Commentary: It is understood that performing the sacrifice first and then shaving the head is the Sunnah (prescribed) order.

Hadith Commentary:
(1)
Imam Bukhari rahimahullah has narrated this hadith in detail at another place, stating that when the Prophet sallallahu alayhi wa sallam finished writing the conditions of the treaty, he ordered the noble Companions radi Allahu anhum to stand up, offer their sacrifices, and shave their heads.
In that narration, it is also mentioned that Umm Salamah radi Allahu anha said to the Messenger of Allah sallallahu alayhi wa sallam: "Do not speak to anyone, get up and slaughter your sacrificial animal." Accordingly, he went outside, slaughtered the sacrificial animals, and shaved his head.
(Sahih al-Bukhari, al-Shurut, Hadith: 2731)
(2)
From these ahadith, it is understood that the mentioned sequence is only in the case of being prevented (ihsar), because in normal circumstances, the sequence is not necessary.
(Fath al-Bari: 14/4)
(3)
In the Noble Qur’an, it is stated: "Do not shave your heads until the sacrificial animal reaches its place."
(al-Baqarah: 196: 2)
The requirement of this verse is that one should not shave until the sacrifice reaches its place, whereas from this hadith it is understood that the head was shaved before the sacrifice reached its place.
The answer to this is that for the one prevented (mahsoor), the place of sacrifice is the very spot where the prevention occurred. Thus, the Messenger of Allah sallallahu alayhi wa sallam slaughtered his sacrifice at the place of Hudaybiyyah at the time of being prevented; it was not sent inside the Haram.
And Allah knows best.
Although some people think that in the case of being prevented, the sacrifice should be sent to the Haram of the Ka'bah, and only after it is slaughtered there is it permissible to exit the state of ihram, this hadith refutes their view.