Getting products associated to custom shipping rates

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we developed an app to export products from the e-commerce to a csv file. Using the REST API we are able to get the shipping zones, so to get the dedicated shipping cost for each product depending on which zone the customer selected in our app.

We are now having a case where a cusomer created a custom shipping rate where he associated 10 products to a specific shipping cost. Do we have the possibility to read this information, so to know that the product has a dedicated shipping cost which overrides the standard one?

The app works only in the backoffice of the e-commerce, it's not meant to show anything in the storefront.