I am trying the exact same thing.
Basically, each store has a Shop Manager that uploads their products etc.
Fortunately I have a static set of Product Categories, so hiding that was simple enough. I have added taxonomy meta for the Shipping classes so we can see and filter which store manager created them.
The issue I sit now is setting up shipping per Store Manager. I understand that you could obviously go into the woocommerce settings and setup the rates per shipping category. But the store managers won’t have access to that page.
It’s a bit of a pickle 🙂