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.
I thought about that, on the other hand, they may be Beau's, which he is said to carry.