Mine just had an unfortunate run-in with a tile floor. I have applecare+ so doing the damage replacement.
At least in the US...
if you take it into the store, they'll send it out and mail it back to the store (or possible directly straight to you) they estimate 7-10 days.
Or what I wound up doing.
Called them, they're express shipping a replacement watch to me, I'll put my old one in the box and return it to them.
They do take a security deposit on a credit card, but will refund when they receive the broken watch.
Gave them my info, and the serial number on the website, hit enter, and my phone rang about 30 seconds later.
Took about 10 minutes on the phone,