It is feasible with the following configurations: 

• Have studio
  
  

• Configure the shipping connector (carrier) that you will use to actually print the labels in Odoo and deliver to your clients. You need to configure it on "Get rate and create shipment" for the integration level, and "Estimated cost" as invoicing policy. Make sure that this shipping method is NOT available on your website.
  
  

• Create a shipping method of your own, either fixed price or based on rules, that will be published on the website. This is the cost for the delivery that your customers will see on the website.
  
  

• Create an automated actions

• On the stock.picking model

• Triggered on creation

•  Applied on Carrier = “Your_own_delivery_method_name”

• Action to do : Update the record

• Data to write

• Field : Carrier (transfer)

• Evaluation Type : Reference

• Record: select the shipping connector your will use

Doing so, your customers will see the price of your own delivery method on the website. But when they confirms the sales, the generated delivery will use the shipping connector of your choice, which will print the shipping labels when the delivery is confirmed.