In order for your body to adjust to the weight loss, you shouldn't lose more than 2 pounds a week. Otherwise, you're going to end up with a sack of sagging skin around your body that will need to be removed in surgery. That's a cold, hard fact. Absolutely nothing you do will tighten that skin again. So, in order to not freak your body out and let you build muscle to replace the fat to keep the skin taught, you HAVE to exercise.
There are no if's, and's or but's about it. Besides, rapid weight loss with fad diets set you up to gain twice as much weight as you lost. Don't.do.it.
Exercise. Even if it's just walking around your neighborhood, the mall or an indoor track at a gym. You'll feel the results and you'll feel better about yourself in general.