Probably a little late here, but I built an app exactly for this purpose. We add anything you can think of to orders between the time the order is placed and it’s imported by other software (whether that be accounting, 3PLs, or other fulfillment tools).
We’re able to configure rules for exactly the situation you describe above! I hope this can help someone else in the same problem down the road.
Link to app: https://apps.shopify.com/pls-smart-pack-ship
Quick video setting up the solution:https://youtu.be/59H6_OAWA6w