Karlie here from the Shopify Support Team! Although the order confirmation notification that is sent out automatically cannot be disabled at this time, you do still have the option of contacting your customers from within the Shopify Admin. I am sorry about the inconvenience here. There is only a couple of notifications that can be disabled, you can check out our guide here to see how to disable and adjust notifications.
If you are still interested in contacting your customers manually, then you can do so by sending them an email from within your Shopify Admin. At the checkout, customers are required to fill in their information and that information gets added to your customer list.
To email or contact a customer, you can do so by following this guide or by following the below instructions:
I hope this has answered your question. If not, or if you have any further questions please let me know. I will be happy to help!