The solution is to create different skeletons for each distinct body part (head or legs or whatever), especially when you need them to move and animate differently, and have different bones.
You don't need to use Skins, but also you have that option to use Skins in combination with the above solution if you want.
There's a planned feature called SkeletonAttachment (basically attaching a skeleton to a bone of another skeleton), and that would've been the right way to combine those different parts. But that's pretty far away in terms of when it will be added to Spine since it's a pretty complex feature to add.
But right now, at runtime, Spine-Unity has tools that allow you to let any GameObject follow any of the bones on your skeleton. So you can use that to manually combine different Spine GameObjects in Unity editor, and also play the right animations together by controlling those many different SkeletonAnimation components together.