Shipping cost Problem

I’m not sure how to do this but my client has a products that varies in sizes and weights and its hard to calculate shipping cost charges, is there any option in woocommerce that when customer comes into checkout page they have to send first an email to us asking for the shipping cost for the item? also can woocommerce disable checkout if there is no supplied shipping cost?

any suggestions is highly appreciated

Thanks

https://wordpress.org/plugins/woocommerce/