There are a few possibilities on how to implement this feature:
1. A Windows, Linux or MacOS console application:
- Runs on a PC
- Command line interaction, e.g. you run the application with <program-name> <order-id>
2. A Web-based application:
- Runs on your PC with a configured web server or on your webhosting
- The user interface is a HTML 5 Bootstrap website where you enter the order-id
3. Others
Comments:
- A private shopify APP can access your store
- You can manage the API credentials in your Shopify Admin
Questions:
- Where do you want to run the application?
- How do you want to interact with the application?