You have to decide what you really want from the ceremony.
Disney's services provide a nice space, a person to do the ceremony, etc.
You can do what the other poster did, and use a space elsewhere with a non-disney provided person.
Or you could just pick a spot, stand with each other and speak the words you want to speak, and not pay a dime. You don't need any sort of officiant to renew vows; they don't have to be licensed or a minister or anything. There is no legality involved. So it could just be YOU.
In our personal case, when talking about a renewal (discussion started at our wedding, which was created for my husband and had very little to do with ME b/c I wanted Vegas), we wanted the whole thing again...the flowers and dress and CAKE...but way fewer people with no obligatory invitations and not having to worry about possibly offending various family members with what we REALLY wanted to do.
While some of the spaces Disney has are nice, I tend to love the spaces they reserve for the BIG weddings/renewals. Alas you can't book those for teensy events.
But...Dis'er lurkyloo has a great blog in which she gives details on lots and lots of things, including how to plan a
small private event at WDW. While you probably couldn't also have a minister come in and be obvious about a renewal, it might make for a nice space to say your words to each other, and maybe have some food afterwards.
