Nick here from Shopify.
I'm thinking the best way to go about this would be an app from the Shopify App Store with a print on demand (POD) app. A POD app is pretty much what you've described in your topic, it's when you can create custom designs of various different products where the app company would create each product individually on demand as it is ordered and ship it straight to the customer, so you wouldn't touch or see the product at all. There are a variety of different POD apps in the app store and it would probably be worth your while to look through and research them to find the one you like the best but also the products you want to sell. Some focus heavily on t-shirts which I see you aren't keen on, but others have a wide variety of different products you can sell. Let's take a look at some of the POD apps I like the best:
Do you think an app along these lines is what you'd be looking for?