EasyRoutes doesn't currently offer a customer-facing "pick a new date" self-service tool. In practice, customers reply to your delivery notifications or use the contact details on their branded tracking page to reach you; you then move the order with Send to another route and send the Rescheduled notification with the new details.
Delivery Ratings and tracking pages keep the customer in the loop throughout. This flow is the same in EasyRoutes for Shopify and EasyRoutes for Web.