@cam2363 ,Cameron, Chances are the lens on watch may be acrylic/plastic and if you have access to, or willing to purchase what they call a headlight restoration kit, I believe would work well and would be able to use it on other devices possibly as well to remove scratches. If your watch has a lot of buttons on the face, this may be a pain. If going to try the kit, keep the pad moving, a little damp and low rpm as you do not want to burn the watch face. I will post a couple links below to give an idea of kits available, you can also check out U tube (headlight restoration)to see it being used. Good luck. I hope this helped you out, if so let me know by pressing the helpful button.
http://mycarneedsthis.com/best-headlight-restoration-kits-to-buy/
https://www.walmart.com/ip/3M-Headlight-Restoration-Kit/13023890