Actually, you should not even be speaking with USPS. You did not contract with them. You contracted with Apple. Apple agreed to have a product delivered to you and, consequently, Apple contracted with USPS for said delivery. Your dealings should be with Apple and Apple should deal with USPS.
I am very surprised that they chose USPS. My Apple products (including the watch) have always been shipped via Fedex.
For the record, something similar happened to me several years back. Apple replaced the product immediately. The same thing happened last week with my wife dealing with QVC. She already has the replacement product from QVC.