We don't have any equivalence to "celebrant". It's more of a cultural difference.
신부 means 'father' (catholic church), and can be mistaken easily with the homophone 'bride'.
성직자 roughly means 'cleric', virtually all people making their living on religion of any kind.
Therefore my best bet would be '사제' = priest.
집전사제 would be a rather appropriate pick.
"집전사제께서 우리 결혼식을 주도/진행하셨어요"