The usual approach would be for you to provide what Shopify calls a fulfillment service in the merchant store. If you are a fulfillment service, then the merchant can choose to fulfill line items sold in orders with your service. You would then be able to provide fulfillment information like tracking numbers etc.
But it gets complicated pretty fast. Your involvement with Shopify to master being a selectable courier can also be done via becoming a delivery option in the merchant's shipping selections. Again, for that to be a reality you have some complicated work. Not easy.