I have now received two watches, and they both shipped basically overnight.
For the 42, I woke up on 4/29 to find that it had gotten charged during the night and was preparing for shipping. It shipped in the evening of 4/29 and arrived on 4/30.
With the 38, it was charged / shipped on Friday (May 2), UPS flew and drove it all the way to NYC by Saturday morning, where it sat all weekend and was delivered today (Monday). If it had been going to an address where they had Saturday delivery, it would have been delivered on Saturday.
When the watch ships, Apple will give you a tracking number, and you can follow it as it moves through the UPS system, so you would know if it is coming tomorrow or not -- you don't have to wait for the UPS truck to come before you find out.
Good to know on the overnight stuff.
It's nearly 2PM here in Ohio, and I'm still in "Preparing for Shipment" mode. Depending on where it is coming from... I'm pretty doubtful I get it tomorrow. You had some good luck though, so I'll hold out hope.