Have you taken it to an Apple store or called their support line? They could probably tell you how much an out-of-warranty service would cost. Get a written quote from them.
If you purchased the watch with a credit card that has extended warranty services, set up a claim with them. The steps for filing a claim differ for each credit card, but they should be able to tell you exactly what to do.
They might ask you for the service quote, or they might just refund you your entire purchase price for you to buy a new one.
That's what I would do.