Usually, when I order something online, I get an receipt via mail and paper (with the shipment). Mail and paper receipt contain order details which can be used

Usually, when I order something online, I get an receipt via mail and paper (with the shipment). Mail and paper receipt contain order details which can be used to prove the legitimacy. And you can always sign the receipt (plain/text or attachment with the mail, QR code with the paper receipt). It is important not to delete the order data, but to anonymize the user data. Your shop software should be able to handle this. Otherwise, I would use another product ;)