LIkely the best option is to go into Shopify custom fulfillment options to set up a new fulfillment service.
From here you need to set the fulfillment option on the variant of each item, as products and variants are treated differently with the Fulfillment options.
Here's a guide on setting this up: https://www.skusavvy.com/blog/how-to-setup-shopify-custom-fulfillment-service
Another option is to use something like SKUSavvy.com which will automatically connect to your Shopify store and coordinate the pick pack ship operations while updating Shopify details along the way. There's one free account included too.