Ray-
If you can, look for the latest episode of This Old House Hour or Ask This Old House. Rich Katheury shows how to repair malfunctioning valves in a lady's shower, with single handles like you indicate yours is. It should broadcast everywhere tomorrow, Saturday. Check your local listings for time. Season 12, Episode 21.
Unlike Rich in his effort, I would have configured some contraption to hang down inside the wall to catch any dropped parts; lose a part such as the valve seat in there, it's gone and back to the store you go, guessing as to the right part number.
Plus, once the faucets and escutcheons are off, I'd leave them off and the shower door open in a heated coach for several days to try and dry the inside of the wall as much as possible before closing that wall again. If not dry, mold and rot may result from trapped moisture in an unventilated place. It may help to remove the small vent/access plate in the shower kick wall below the door; the more air under there and the longer the better. With a flashlight you should be able to look in that port to monitor any apparent wetness.
Joel