Jump rings ?
Typically a ring used to join two separate pieces together, like a stone to a chain in order to make a neck pendant. Or a better example is joining a charm to a bracelet. Usually split, so it can be opened and closed again once the linking has been accomplished. Not sure of the exact use in the OP context, but jump ring is very common term in jewellry making.
-frank
Even if you cut a kerf in the mandrel it might not hurt the winding operation.
A thin Walter zip-cut or two will do the job.