This app was mentioned in 4 comments, with an average of 1.75 upvotes
You can sideload nearly any app onto your watch via ADB, so you could obtain an APK of something like this Power Schedule app and install it on your watch. Maybe it'll work, maybe not.
Just checked, regular Android clock app doesn't offer that option. My bad ._.
EDIT: A quick Google search led me to Power Schedule, an app that lets you choose time when your phone will turn off automatically.
Do you have a set work schedule? I use "Power Scheduler" to set my volume to mute, wifi to off, and GPS to off, then turn everything back on when I leave.
I have found these
https://play.google.com/store/apps/details?id=com.monocube.powerschedule