Set Custom Shipping Profile via GraphQL/REST to Ignore Product from Cart Subtotal

[Chad-RP]

We have setup Shipping Profiles based on cart total. There is one product that is not shipped (digital product) and would like to exclude it from the subtotal when calculating shipping. Currently, customers get free shipping if order total is over $1000, and this product is $200. I've been looking into GraphQL shipping profiles to adjust this. Would it be possible to get the cart lineitems, if this product is in there, remove from subtotal and recalculate which shipping profile to use?

I know I can call all of the shipping profiles via GraphQL and get the cart line items as well, what would be the call to set the shipping cost in the checkout? I have a private app setup and need it to call out to the php script and recalculate the shipping total.