I don't think it is practical to expand the perimeter of a hollowed out coin. Even if you can expand part of the edge, the junction between the edge and the face will be rounded.
You might have success by cutting away the interior of the coin leaving a rim and then stretching that so an OEM coin can fit inside. A third coin would be faced to a thin disk and silver soldered to the expanded rim to create the container. There will be a small line of silver solder corresponding to the clearance fit for the OEM coin but it should be unnoticeable under casual inspection. Before facing the coin, the edge could be worked to expand the diameter slightly for a closer fit.
As I recall, it was John Saunders, NYC CNC, that did a video on cutting down a coin. I believe that he glued the coin down with super glue.
I would mount a piece of aluminum in the lathe and machine a pocket for a snug fit of the coin. Then, I would glue a coin in with super glue and machine the coin. When finished, the assembly can be trimmed to remove excess material and the remainder of the aluminum dissolved away with a dilute sodium hydroxide solution. The super glue can be removed with actone or, more quickly, with Goof Off ™ super glue remover leaving the machined coin behind.