Since you don't plan to remove the mounting at this time, just a measurement would help.

If it is a small hole, it is probably not an ojime -unless it was intended for a ladies' or children's ensemble. Tucked into the front of the obi, ladies and children's inro ensembles had ojime with holes larger than most beads in the same size. And, ordinarily, should have a non abrasive opening. This would provide less wear and smooth passage for two inro cords.