I had a customer who just filed a “non-receipt” chargeback 2 days after he placed his order, even though the quoted delivery timeframe hadn’t even passed yet. I immediately contacted him, and he said the reason he filed the dispute is because he never got an order confirmation email (it was definitely sent), and he couldn’t remember the name of the website where he had placed the order, so he assumed he had been scammed. 
Anyhow, he said he would call his bank right away to cancel the dispute, and he sent me an email 5 minutes later to confirm that he had cancelled it. However, it’s still showing up as an open dispute in Shopify and it says a response won’t be submitted to the bank until May 20th. If I ship the item and submit a response, including proof of delivery as well as the email from the customer saying he had cancelled the dispute and wants to proceed with the order, is there any way to get Shopify to submit the reply sooner than May 20th (3 weeks)?
But even in doing that, I’m slightly concerned that there’s still a small possibility that the dispute would get somehow still get resolved in his favor and then I would be out the money and the product. Or, alternatively, would it be better to just cancel that order and have the customer place a new order?
It’s a $700 order and as a small business that’s a lot of cash to have tied up for so long; it’ll probably be 5-6 weeks before it gets released based on past experience.