Update customer with changes in estimated delivery details

My topic title may not explain this well, so here’s what I’m trying to do.

I’m using WordPress with WooCommerce.

I’m with a clothing brand that sometimes has to wait on backordered supplies of fabric and other materials, so the estimated delivery date of customer orders sometimes takes longer than normal. I’m looking for a plugin or extension or another way to make it possible to send customers notifications if there happens to be a change in their expected delivery date. I’m not talking about changes in delivery date once our shipping service (USPS or UPS) actually picks up the package, it’s for notifying customers if their order is going to be delayed in leaving our headquarters. Any idea of how to do this besides just sending them a customer note from their individual order pages in WooCommerce?

Thanks in advance for the help.