Q - being in the "old and cranky" department qualifies me to give you cheap and effective ideas to help you solve your perceived problem. A cheap, effective hair packer is one made from a larger coat button, drilled in center to accept fine diameter pan or roundhead screw, mounted on dowel rod drilled on center to accept said screw glued into dowel. Takes more time to make than going out to get an inexpensive plastic Griffin four hole packing tool, but...
Another method is to use a small diameter washer. Your drilled coin only needs to have the rough edges relieved (rounded) and it'll work fine.