I cannot help but think that if you are wanting to reduce your body fat to below 10% - you really want to preserve as much muscle mass as possible...
A water fast would surely be the last thing that you would want to do because you would spend the next month basically eroding your muscle mass... You surely want to retain as much of that muscle mass as possible - not only for good health but to fill your skin as the fat disappears.
I would have thought that you would be much better served to eat a definite level of protein within a balanced diet at an appropriate calorie level for weight loss.
This, combined with exercise will bring your body fat down.