I would go along with the Ball & Shot idea. It would be flipped up & used for Ball & down thus unused for shot.
It is true that small apertures increase the depth of field of the focus, but equally true they Dim the visibility. Very small apertures are primarily for use on target guns under good light conditions, in the Field, the bigger ones are better.
I was never good with open sights, but successfully squirrel hunted for several years with a .22 equipped with the old Williams 5D sight. I would sight in with the little hole, then screw it out & just use the large threaded hole for hunting. It shot to the same place but gave one much better sighting in the early morning or late afternoon under low light conditions when the squirrels were most active.
Also, the closer to ones eye the peep is the better. To use one on the opening lever though it would need to be on a gun which the lever was always centered. On a gun with wear compensating bolts where the lever goes left in compensating the point of impact would change with lever position.
