Both our cats are "studio" cats. Forrest stays in my recording studio all day, and Lilly is in my Husbands studio. We do music, sound FX and anything audio so our cats are subjected to sounds all day long.
They can get up and leave if they want and go into another room but they never do UNLESS the music or audio is extremely loud. I can't imagine that the "clinking" sound of the rings hitting together could hurt the cat's ears. If it did I bet it would go into another room as fast as it could. It is probably just annoyed by it.
I wouldn't worry. Maybe Nacho is telling you he wants to be in the magic show