There is not currently a way to do this for WooCommerce. But we are actively working on a feature that will allow you to show the rates you get in ShipStation to your customers. It's currently available for Shopify and BigCommerce stores and we'll be adding more selling channels soon. You can review information about this feature in our In-Cart Delivery Options article.
We will update that article each time we add support for additional selling channels, so keep an eye out for WooCommerce support.
I would like to see this as well. In many cases, it's the difference between an order (that gets shipped via ShipStation) and no order. I will also note that this feature has now been in development for THREE YEARS.