The Mishna (Zevachim 3:1) states:
כל הפסולין ששחטו שחיטתן כשרה שהשחיטה כשרה בזרים בנשים ובעבדים ובטמאים אפילו בקדשי קדשים
Anyone who is invalid for Temple service who slaughtered [a sacrifice], the slaughter is valid, for slaughtering [sacrifices] is valid even for non-priests, women, slaves and even impure people, even for the holiest of sacrifices.
So yes, any adult can slaughter the sacrifice. If anything, it is best if the owners themselves do the slaughtering, as there is a principle מצווה בו יותר מבשלוחו that it is preferable to do one's Mitzva one's self and not to send a messenger. Much ink has been spilled debating if that principle applies here or not, but all agree that nearly anyone can do the slaughtering, certainly bedieved.
The Rambam codifies this rule in Pesulei Mukdashin 1:1, noting that children are invalid for slaughtering sacrifices, as slaughtering sacrifices requires certain specific intentions, and impure individuals should not slaughter sacrifices ab initio lest they accidentally come to touch the meat and render it impure.
Interestingly, the only instance in all of Halacha TTBOMK where a non-Jew can slaughter an animal (Shechita) is by way of offering his own burnt sacrifice (Olah) to our God when outside the Temple. He can even do this nowadays if he wants (Rambam Ma'aseh Korbanot 19:16).