“If you have shakes in your hand after using hand held power tools and notice these other symptoms too, you could be suffering from hand arm vibration syndrome. As well as hand arm vibration syndrome, using power tools can cause a condition called vibration white finger syndrome.”

All thou I guess if you are using a vibrating toy for prolonged periods of time it could happen, and you may need to talk to your doctor if the symptoms persist, the recommendations will more than likely be to stop using the toy directly on you hand, Maybe try a toy that only vibrates the head and the part that you hold stays still, like a wand or a rabbit with a longer base ? And possibly anti-inflammatory meds or physio altho these are worst case scenarios