The only approved repair for Apple Watch is via Apple, and they don't supply parts outside the Apple Approved Service Centers. I think you are stuck with a costly repair.
If you look through the photos in this thread you will see there are two clear patterns of damage,
1. A crack all the way around the edge of the screen, leaving the screen separated but in one piece. This seems to be typical for screens damaged by pressure from behind due to an expanding battery, but it could occur from external impact. The crack starts small and simply grows along the line of least resistance.
2. Screens with multiple cracks, running in several directions across the face, sometimes the cracks are so extensive they look more like they were hit by a truck! This is typical for external impact (including dropping) or crushing from the outside. It would be very unusual for multiple cracks to be caused by a swelling battery because the display and logic board are bonded to the front glass and act as a load spreader, so the force is concentrated around the perimeter and a type #1 crack occurs.