Symbolic Wedding in Venice

As you have a very specific location in mind, it is doubtful that anyone else will have the exact information you need. I would suggest contacting them directly.

http://www.scuolasangiovanni.it/index.php?page=31&lang=en

Here is the events contact page for the San Giovanni Engelista Servizi. Who knows?
http://www.scuolasangiovanni.it/index.php?page=32&lang=en&parameter=sale#terra

Good luck. If they are willing to work w you, there might be only a few specific times available around their mass and tours schedule. Dont suppose ya'll are already having a catholic wedding here in the US? hard telling how open the parish will be to working w you. Emphasize that you are being legally married in the US. Part of me wants to suggest that you just ask for a "blessing"..... the other part of me suspects that my local Catholic parish here probably wouldnt get involved in "blessing" a marriage they had not duly counseled.
What specifically are you hoping for? some lovely photos? a chance to recite vows (perhaps not in front of clergy, that might be the thing that makes the church comfortable, perhaps they willl provide you w a nice docent). if you are wanting some sort of certificate, that might NOT be something the church would be willing to provide.
I could be pessimistic, perhaps churches in venice get this request all the time......

The Catholic mindset about marriage is very strict. These are the general guidelines:
- churches are for praying, not for photo opportunities
- marriage is a lifelong bond to be approached very seriously
- the most appropriate place for a marriage is the parish church of one of the members of the couple, where they will be likely known by the local priest that can guide them
- marriage between a Catholic and a non Catholic is possible but subject to even closer scrutiny, involving a permission from the local bishop office
- marriage between two non Catholics in a Catholic church is completely out of question (I have seen a case in which outlandish sums of money were offered to break this point, without success)
- in Italy, a parish priest has also the status of public officer as the marriages he performs are recognized by state authority, so he must stick also to state rules.

Under this mindset, a symbolic wedding in a Catholic church is extremely improbable. I am writing this not to discourage but to make you understand the mindset: the closer you get to this mindset, the more leeway you are going to get. For example, wife and me got married out of our parish church, that is often difficult; but both parishes got duly involved and we approached our chosen church with a believable reason to get married exactly there, and there only - so we experienced little difficulties. The parish priest felt overworked so asked us to provide a celebrating priest on our own; he was from my wife's parish, reinforcing the idea that we going to do things the right way.

It is quite common, in Italy, to add a blessing to a Mass for a couple in important anniversaries of their marriage - say, after 25 of 50 years. Sometimes extra rings are exchanged. If they are practicing Catholics in their parish church this will come very natural, but I do not know how an unknown foreign couple would be approached. A letter of introduction from your home Catholic church could help.

lachera said it best. If you are Catholic AND being married in a Catholic church ask your priest if he would write a letter requesting a blessing of your union there.

Al, im going to chime back in, hopefully that church has an outdoor sign of some sort similiar too what we are accoustumed to seeing in the U.S. buy yr bride a nice bouquet of flowers and get some other trustworthy tourist to take photos for you as you pose w the Evangelista sign. Then take yr bride out for a fancy lunch.