It may make a difference when you are walking (spring, summer, fall, or winter) and how far you are intending to walk. That's assuming you want to have the ceremony during your Camino. If you want to have it before or after, what restrictions on where you have it? Maybe somewhere further along the route that can bring back happy memories when you return.
You also say that you don't think in a cathedral is the right place since you aren't Catholic. That may hold true for other churches I might be inclined to suggest. One alternative you may want to consider is to have the ceremony on the church steps. That was not uncommon as a medieval practice, I've been told (in keeping with the medieval origins of the Camino). With those ideas in mind, a few suggestions.
- If you want to have the ceremony during your Camino and not inside a church, perhaps at (but not inside) Eunate might be a good idea. That is a little off the beaten track, is interesting to look at, and is easy for guests to reach by taxi from Pamplona, which is itself a fairly big city by Camino standards and easy to reach by bus or train. It also has a mysterious history.
- Another option if you want to have the ceremony "on the church steps" might be Fromista. There is an exquisite Romanesque church surrounded by a large open plaza. It is still in the first half of the Camino, shortly after Burgos.
- If you are going to have the ceremony after you are done walking (assuming you are walking about half, rather than two thirds or all), then a couple of non-church options come to mind. One is at Hospital de Orbigo on the long bridge. The bridge has a very romantic medieval history where a knight (accompanied by some friends) jousted for days and days, taking on all comers to prove his love for his lady. It is also a very picturesque location. You can try and ignore the fact that after all of the jousting, his lady ended up rejecting him.
- Another non-church option a little further along is the Donativo stand that David runs just before Astorga. I think that would be a great place for a wedding ceremony.
- Finally, you could consider having the ceremony at Finisterre or Muxia by the Atlantic. Then next Camino you could walk to your wedding site.
Just a few ideas. I hope you have a great Camino and a long and happy life together.
Ultreia!