A cat's life in the wild is a brief, painful, fearful thing. You spared your kitty all that. You made sure River had a long, healthy, happy life ... and even at the end, you made sure River went with as little pain as possible.
When you're being pulled into grief, sometimes you can instead opt for gratitude: you had the privilege of River, and nobody else has been quite that lucky. So don't forget to thank River for all the years together.