Hi Geravin, I'm also in the same position. But most churches are adamant about this.
One solution I considered was getting a civil celebrant to witness the paperwork to make sure it's legal, and then getting a Christian friend who's an elder or a mature Christian leader, to say a few words, preside and pray for the couple as a Pastor would.
It is not against the law who presides over a wedding, as long as the paperwork is done and approved by a licenced solemnizer. And the bible doesn't specify that only a Pastor may preside over a Christian wedding; I know many friends who've been in faithful service to the Lord who are not pastors. In fact, it might make the whole ceremony more personal that moving that way, having a close friend perform the religious part of the service, while the civil celebrant legalises it.
So your first option would be to find a pastor to do it; second would be to find a Christian celebrant from the list of approved solemnisers (I wouldn't know which ones are but you can check the other threads for help or ask each one as you go down the list) and the third option would be to ask a close mature Christian friend to preside over the religious aspects while the civil celebrant is there to make it legal!
I think we're likely going with the third option. Planning to ask our Christian marriage counselor or a Pastor friend to pray and bless us, while the best man's dad (who happens to be a civil celebrant) to witness the whole thing.
Hope this helps. Good luck!