When my DH and I were getting married it was not my first and I didn't want a big giant to-do. When we went to town hall to ask about the information needed for a marriage licence they were actually able to provide us with names of people who were able to perform the ceremony. The one we selected was a retired judge who lived in town. We actually got married at his house - he has a lovely garden room with a painted armoire that we stood in front of - our pictures were actually very nice. My brother and good friend came along to be our witnesses.
Years later my sister used the same judge for her wedding - and he came to the small catering facility / restaurant and they got married at the end of the dock. Her neighbors had the same judge marry them a couple of years after that - he came to their home and performed the ceremony in their gorgeous backyard - and the caterers had a lovely brunch in their garden following.
So please don't panic! There are options. Call your town hall and see if they have a list of people - google judge, jsutice of the peace, etc. ask around - you'd be surprised.
Now - almost 16 years later, we wish we had gotten married in a church - so perhaps we'll do a vow-renewal at some point in the future at a church.
Best of luck!