Filter products that has a shipping class

I want to add a check-box to the Woof filter which filters the products that have a shipping class. Any class or specific class is OK. What meta key I should use and how should I set it up.

On the page above I set the check-box and labelled it but I need the above information to set the filter, I think.

The page I need help with: [log in to see the link]