It has been a while since I have used WooCommerce so my terminology may be a little off, but here it goes…
In WooCommerce you have the ability to create shipping classes, these when assigned to individual products will dictate the shipping options available for those products.
There are a number of plugins that further enhance the WooCommerce shipping system, but if you go to WooCommerce > Settings from your site’s dashboard you will see a section for shipping and within that you can set-up your rules to charge certain fees, or disallow shipping altogether for products based from your shipping classes set against products.
Not sure whether that helps at all. Hopefully it points you in the right direction.