You can actually create separate shipping profiles for your products, so that you can have product-based shipping rates. You can learn all about how to set up your own shipping profiles here:
To expand on @pvoulg's comment, you can then use Automate Shipping Profiles to bulk assign your products to their respective Shopify shipping profiles. If you have a lot of products, this can save you hours, sometimes days - we've saved a combined 48 years' of time for Shopify merchants so far. Since it doesn't do rating at checkout, you don't need to upgrade your Shopify plan or pay a $20 extra monthly fee to Shopify to use the app. You simply bulk assign products and uninstall when it's done.