scratches on my watch

Apple has a standard 12 month warranty only for manufacturing defects, which can be extended to 2 years with AppleCare+ with added cover for 2 incidents of accidental damage. However, AppleCare does not cover cosmetic damage and most scratches do not impair the function of the device, so even with AppleCare it is very unlikely you would have any options to have Apple replace your watch.

That feeling when you get that first scratch on your Watch... oh it's no fun.

There are screen protectors and protective cases for the Apple Watch from third party companies, but I can see that won't help us at the moment.

Scratches are cosmetic accidental damage and therefore not cover under the 12 Month limited Warranty. If you have AC+ on the Watch, The display has to be broken to have the Watch replaced under AC+.

Excerpt from the Limited Warranty: This Warranty does not apply: (a) to consumable parts, such as batteries or protective coatings that are designed to diminish over time, unless failure has occurred due to a defect in materials or workmanship; (b) to cosmetic damage, including but not limited to scratches, dents and broken plastic on ports unless failure has occurred due to a defect in materials or workmanship;

No you cannot.