We move side by side humming or singing. It's a gesture we do when we enjoy or like the act of singing.
This happens to our head when we are not standing.
I want a term/phrase for the action when we move our body or head from side to side. I also doubt - it's not side to side (as we do in saying 'NO'). I may better call it 'tilting'. A tilting of head/body from side to side? I'm not sure!
Example is this video. Check the kid. However, he's not shaking his head probably because he's singing. But you get an overall idea.