Swap the ring to your right hand at any point during the morning, or even in the car to the church / venue. And then change it back when your in the car to the venue or whenever u want, u might forget to change it with everything going on but im sure you'll notice once your sat having the wedding breakfast. U can wear them whichever you want, i would prefer wedding ring at the bottom and engagement on top. But a girl i work with wears them the other way round, looks different, but nice