Hi Grace
For someone without faith I cant understand why they would want to come to Church for a wedding because it would be just an old building filled with meaningless objects.
Hypocritical No, because the Church is always there to welcome you and not judgemental when you need it. However, to participate in the rituals of a faith you need to share its faith.
In faith, Marriage is a deeply religous union, for the most part for once and forever. Its considered a gift from God. Like baptism you only get to do it once because you cant keep asking for gifts!
Marriage is probably the only civil contract you cant renegotiate. Most contracts you can update or amend without breaking in law. However, as a Civil contract you either have it or divorce to break it.
I dont think you would be able to re-marry the same person without a divorce anywhere in the world. Actually this might be problematic for the juristiction of the marriage and under which Laws any future problems might be settled.
You can restate your vows in front of witnesses but I cant see any Civil Authority bringing legal authority to doing this.
However a blessing by the Church should be possible, either as a faith based marriage or a blessing if you share that faith.
Given that this isnt what you want I go back to the idea of restating your vows in front of friends and family as witnesses.
Dont know what else you can do.
Thought this might help people interested in getting married in Corfu.
http://www.weddingchaos.co.uk/wedding-abroad/greek-wedding.asp