Could one bend a copper or brass wire to the right shape? I made my own rings for chain mail years ago. Just wound the wire around a steel rod to make a coil and cut it into rings. Wire this thin should be much easier to work with.
Perhaps a piece of soft plastic tubing could be trimmed to fit. If nothing else is handy perhaps a ring cut from the neck of a plastic bottle of some sort. Plastics used for shampoo bottles is usually very soft.
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