My situation is a little unusual.
My wife is a Catholic, and her two girls were raised as Catholics.
My wife had her first marriage annulled - this means that it is 'cancelled' by the Pope - literally, it has to have his approval. That means that in the eys of the Catholic Church, my wife has not been married before - even though she has two children from that marriage! That meant that when we got married, we were able to marry in our parish church - full Nuptial Mass - con-celebration (two priests) the whole nine yards, with the girls as bridesmades.
In my view, this is a perfect illustration of the ability of the Catholic Church to close its eyes to what it prefers not to see.
As preparation for the wedding, because I am not Catholic, I had to produce a copy of my babptism certificate to prove baptism, even though it was not a Catholic baptism, my parents were C of E.
I had to go for two 'chats' with our priest Father Tolkien (son of J.R.R.) about raising as Catholics any children from our marriage - and giving an assurace to that effect.
i am an aetheist, but I have no issue with my wife's faith, or with raising our third daughter as a Catholic - which we did. Father Tolkien never asked me if I believed in God, so it was never a question I had to wreslte with - not the question, but whether to lie to a priest or not. I think he knew my stance, and preferred to ignore it, and avoid any contention - again the Church is able to avoid such uncoomfrotable sitatuons when it chooses.
To answer your question - I married in church because my wife wanted it, and it was no problem to me. If neither of you believe, and feel uncomdrtable, then i would go, as suggested, with a civil ceremony in a nice venue - which will avoid you feeling uncomfrtable in any way.