I don't know if this will solve your problem, but here's what I am thinking:
You can remove the shipping address portion in your Shopify checkout. All you need to do is uncheck that your product requires shipping. Once you do that, when people go through the checkout process, they will only be asked for billing information and a method of payment.
This way, customers will not have to enter a shipping address at all. I am wondering if this will work with your app that you are using.