That would make one wonder. At Christmas time I played with the rolls of carboard left after the paper is gone. All three of my animals jumped and played with it. I would think that the only way an animal would react badly to something like that is if they've been mistreated with something similar. It just breaks my heart that someone would be so heartless as to hit an animal with their hand, let alone a stick.

Perhaps you can try to work with Luna holding various stick-like objects showing her that you wouldn't ever hurt her with it. Perhaps she'll come out of her shell once she sees that sticks don't mean harm anymore.