Integrating a custom app with the existing Shipping functionality

Is there API documentation on how to integrate with Shopify’s built in shipping functionality?

I had a quick look and couldn’t see anything, it all seemed geared around products, orders etc.

I’m building an app that will determine which shipping method will be used based on products in the cart.

Basically, I want to pass the cart information to my app, review the products in there, and then send back a response to force a particular shipping method (preferably one configured in Shopify).

If I’m able to tap into the existing shipping functionality then I wouldn’t need to build the shipping part into my app, otherwise, if it’s not possible, I’ll need to consider building shipping functionality into my app.