First of all, the priest did not sing Cohen’s lyrics, so you were off base with your comment from the get go
I was responding to your seeming to not think that sexual ‘lyrics’ have a place in a Christian setting. If that is so, then the Old Testament would not have a place there either.
The problem is anybody who is not ignorant of the works of the great Leonard Cohen will automatically think of the original lyrics, which, while brilliant, are out of place in this setting.
As for Song of Songs, it would be inappropriate to sing a song based on those in this situation also. Not everything Biblical is appropriate for singing in church. It's not that difficult a concept to grasp.
There’d be a problem using Cohen’s version anyhow in a wedding; he’s got the sex in the past tense.