Chat or call Apple Support. Tell them yours is broken and you'd like to set up a DIY repair to order a replacement. If they try to transfer you to sales, don't let them, because sales can't help you.Does anyone know where to find an Apple Solo Loop Silicone 45mm band in Cyprus Green size 5. It is my favorite band and mine is starting to show wear. Think I am out of luck. Thanks!
Have your Watch's serial number handy. They'll need that to start the process, and they'll ask what iPhone and iOS version you have, but what you tell them here doesn't really matter in case you want to make something up for some reason. Then they'll ask for photos. You can just say you don't have it with you, or it's broken but doesnt show that in photos, whatever you want to do. Or you can take a photo. either way it's the same. They'll check their parts system and hopefully they'll have your size. If they do, It's retail price plus shipping, usually $10? Been a while since I needed to replace a band so I forget. This is how you buy out of season bands from Apple, subject to the availability of colors in their parts system which changes depending on what Zip/Postal code you give them.
Bonus tip: If your watch has AppleCare, they'll sometimes give you the band for free!