A digital file would need to be added to the Shopify admin as a product of some sort to enable it to be sold as a digitial file directly through to the customer. The most common way would be to sell the digital file through an app from the Shopify App store. There is a Shopify developed app, but some others too and with free plans:
Would this involve what you're trying to avoid?
If not, the other ways to do this could be quite complicated. I'm thinking you email the customer after with the digital file, but that seems like a lot of extra work and hassle. Can you reply and let me know if the digital download apps can do what you need and if not, we can take another look.