I would definitely recommend going with a stateroom balcony, since that is your own private space. You could also order champagne for you and non-alcoholic sparkling grape juice for the kids from room service, and a specialty cake from the cake shop.
If you really want to have the wedding outside your stateroom, I do think you are running a risk, and it would be no fun at all for your wife if you were reprimanded for conducting a ceremony in the public spaces of the ship without permission. This is really not unique to Disney: hotels typically do not allow unsanctioned wedding/vow ceremonies in their lobbies, poolside, or on the beach, as weddings are a big business for hotels. We have a local private botanical garden that is very scenic and they have a similar prohibition on private ceremonies, and they too charge thousands of dollars for folks to get married there. The fact is, if they allow people to get married "for free," then why would anyone pay thousands of dollars for the privilege of doing so?
Also, you know your wife best, but just saying, I would want to know if my husband was planning a vow renewal so I could pick out a dress, do my hair, possibly write my own vows etc. Just something to think about.