I see how to mute the watch altogether, that's not what I want. When my phone rings, my watch also rings. Problem is, the watch doesn't stop as soon as I answer my phone. So I'm talking on the phone and my watch is ringing the whole time. I also don't want to not get ANY notification on the watch of incoming calls (I know that's an option as well.). Surely I can just change the TYPE of alert for an incoming call?
Give this a try on your watch: Go to settings > Sound and vibration > sound mode and change to vibrate.