WHCC provides a simple API to accept orders for processing and production.
Import the order into the Order Submit API and recieve a ConfirmationId in return.
Submit that ConfirmationId to the Order Submit API to confirmation that the order should be processed.
You can see and explore a sample Order Import Request that you will need to generate and POST to the Import endpoint. The Product Catalog will be necessary to understand which products and attributes represent your product.
Import an order to the Order Submit API with data from the Product Catalog