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.
Observing the sequence with regards to the acts of ‘Aqeeqah is only recommended and not obligatory. It is recommended to shave the newborn's hair after slaughtering the animal sacrifice according to the view considered to be correct by some scholars. Other scholars suggested that it is recommended to shave the hair first then slaughter. The Shaafi‘i scholar An-Nawawi said:
"It is recommended to shave the newborn's hair on the seventh day… Should the shaving be done before slaughtering? Scholars held two different opinions in this regard; the preferred one is that it is recommended to shave after slaughtering. This view was held by the compiler (An-Nawawi), Al-Baghawi, Al-Jurjaani and others; and the relevant Hadeeth indicates it. The second view is that the shaving should be done before slaughtering. Al-Muhaamili stated this decisively in his book Al-Muqni‘; and Ar-Rooyaani preferred this view, tracing it back to Ash-Shaafi‘i." [Al-Majmoo‘]
For further benefit, kindly refer to Fataawa 81275and 82088.
Allaah Knows best.