How PC (period-correct) does your wedding couple want to be? Are they sticklers to the last detail or are they willing to say, "Close enough..."? Will they settle for something that is PC within, say, 5 years? 10?

Last summer, I was at a Civil War reenactment with my 4x5 camera. I offered to take some pictures of a group of guys in period dress but warned them that my camera was not even close to being PC. It was probably made in the early 1980s. Not the 1890s. They didn't care as long as the picture looked PC. Even then, there were still a few anachronisms in the picture but they said, "Close enough." --

Point here is to know your audience. If they aren't sticklers, that could take some pressure off you.

As to cameras, I like the Rolleiflex. There are enough models of Rollei made in enough vintages, you could easily get one.
Will there be anybody at the event who could even recognize the difference between a Rolleiflex made circa 1930-5 and one made circa 1950-5? If they did, would anybody care?

However, if you really want to play it PC, get a Speed Graphic and dress up like Weegee!