since you're not terribly heavy, have you considered weight training and intermittent fast to drop the weight?
I'm doing the Water Fast because of detox primarily, and because I am 70 lbs overweight.
But I was able to make good gains prior to this fast by weightlifting and intermittent fasting, and working out while in a fasted state. I lost 15 lbs of fat, and gained muscle, while doing this.
The trick is to use compound exercises that work multiple muscles, and to keep building strength by going up in weight lifted. Squats (most important), benchpress, deadlift, military press, upright rows. These big 5 alone work most of the body. 35 minutes or so to complete 5 sets if you cycle between the exercises.