Can I remove just one app from my Apple Watch?

I'm not sure what you mean by "unpair". If you mean remove it from the Watch, yes, you can do that either directly from the Watch or through the Watch app on your iPhone. If that's not what you meant, please clarify.

Regards.

If you mean the Ring Doorbell/Camera app, there isn't one for the Watch. You can have notifications from the Ring app sent to your watch though. To turn those off, go to the Watch app on your phone, Notifications, swipe down to "Ring" and turn it off.