Walking is great during a fast. I used to walk laps on a high school track near me for an hour or so every morning during fasts.
Unless you have a very specific reason to limit water intake like a dry fast or cutting for your next bodybuilding competition there is no sense in limiting water. Water is your best friend for weight loss. If you aren’t active you don’t need very much, if you are active with exercise or maybe you have a physical job then you will need more water.
My point is, if you feel thirsty drink some water. Water is not your enemy as much of this community might believe.