I love Mr Woods but he is incorrect here, there are rosary bracelets and rosary rings. I think you might have mentioned bracelets earlier.
You are correct about the bracelets made to represent a decade of the rosary, but no one wears a whole rosary.
I remember how shocked I was when Madonna did it.
I think as a Catholic if I had my rosary beads and liked to pass the time by saying a few Hail Mary’s in the limo or on the plane, I might wrap them around my wrist as a place to keep them whilst otherwise occupied. So my thought was old Joe is pretending to be a Rosary saying Catholic who likes to have his prayer beads with him, because I know he ain’t that. Maybe he was planning to wave them around if his Catholic credibility issues came up.