You can learn to shake things without the head shaking. I do it daily. We drink non-homogenized milk and the cream settles. I have had to learn to shake it without shaking my head. It's simply a matter of stiffening your upper body.

The violin playing should not be a problem from what I understand about it. But, if you have an upper neck issue that is unresolved, the stiff neck holding the violin may be an issue. I've see violinists put a folded hand towel over the need of the violin so they do not have to bend the neck as much to hold the violin.