Jerry, if you drill diagonal holes into the joint so that you can get near or into the space that's left at the bottom of the mortise and the tenon doesn't reach quite that far, you can inject ACC glue (Superglue or Krazy Glue or similar) into the joint. Without having one of your shutters to look at, I would guess that a 1/16" or 3/32" hole would be about right and the gel form of the ACC glue will probably be easiest to use. Try to just get enough glue in to glue the joint and work with the stile down so that the glue doesn't go everywhere and glue more of the shutter together. When you got that done, you can put a dab of automotive Bondo or Minwax High Performance Wood Filler into the holes that are left to seal them from the weather or any water that might be around and just to flush the surface back up. I would not totally disassemble the shutters unless there was no other way or I was totally refinishing historically important shutters. They can be difficult to reassemble.