Humans lose moisture for a variety of reasons normally, you don’t need to be sweating in order to lose it, although that obviously drives the loss rate up. You lose a ton of water through just breathing.

On your walks you’re probably burning glycogen, the carbohydrate we store in our liver and muscles for easy access energy, and exhaling a lot of water. We store about half a kilo of glycogen which is then bound up with 3-4x as much water still. While you’re not likely to consume all your glycogen in a 20km walk (you need a marathon to do it), burning a decent chunk of it on top of normal water loss isn’t an unreasonable hypothesis.