Kassey here from the Shopify Guru Team! You can use the Zebra GC420d printer, but unfortunately the GX420d isn't a supported printer with Shopify at the moment! I'm sorry about that, Ed! For more information, you can check out supported hardware here and to learn more about the Zebra GC420d, check out this doc.
I hope this helps, but if you have any further questions - be sure to reach out to Shopify support!