Sometime couples will have a civil ceremony in their own country, but they want the frills, the photos, the dress etc. as an exotic location like the Cayman Islands. My own daughter did this a few years ago. I wrote a special blessing ceremony for her which had contemporary, spiritual vows, readings etc. but which honoured the fact that her "real" wedding had taken place two weeks earlier. Her father walked her up the aisle, but he did not "give her away" he simply gave her the benefit of his arm and his protection on the way to meet her husband.
So, the rings, which they had been wearing for a few weeks? Each took off their wedding ring and handed it to the wedding celebrant (her grandfather!) who blessed them and handed them back so that each could place them back on the other's finger while repeating promises which they had composed.
Now the only thing they have to decide is which date to celebrate as their wedding anniversary.
Knowing my daughter, she'll celebrate both!
Your relationship is very precious, and your wedding ceremony should honour that. So if you want to have a traditional ceremony, or an un-traditional ceremony, find a celebrant who will treat you like the individual you are, and take your wishes into account.