Fasting won't prevent loose skin, and if you do Water Fasting until you hit your goal weight it will add to the problem.
To avoid having loose skin from losing weight you would need to go at a much slower rate of losing than a Water Fast and make sure you get in enough protein to prevent losing lean muscle mass which on a Water Fast you lose along with losing stored fat cells.
On the plus side though being young will be helpful with having your skin bounce back and with exercise and weight training you'd be fine.
Have you thought about just doing a 7-10 day fast to jump start your weight loss plan then switching to calorie counting and exercise?