Return a Product's Shipping Method

[MattDwyerDev]

I'm trying to set up in the product.liquid template that if a product belongs to a certain Shipping Profile, that it will render a certain template. I'm having issues with trying to find the object that returns the shipping handle/title/method of a product.

I've tried using the shipping_method object (https://shopify.dev/docs/themes/liquid/reference/objects/shipping_method), however, no luck (see screenshot below) and there doesn't appear to be any specific object in the product I can return. 

Any help or recommendation on this inquiry would be greatly appreciated.