This is and will be one of my greatest concerns too until the day comes when im at goal and go.. hmmm.. no sagging skin.. lol..
Ok so here is the deal.. it really depends on your body how much weight you have to lose, how long you have been at your weight, and YES IT DOES MATTER IF YOU WORK OUT OR NOT!
Here is why.. pregnant people get big and then it goes away in 9 months, now for someone who has been big say for the past 10 years your skin has stretched and had to carry that weight for a long time. which means its probably lost some of its resilience. It also depends a little on genetic make up and age. the younger you are and the more oily your skin is the less likely you will have to have an excess amount of skin.
For most of us we are going to have some type of excess skin, however by working out you are replacing the fat loss behind the skin with lean muscle which will even out a little bit.
I go to the gym 5 days a week doing not only cardio, but weight training too so that i can help my body along the way. so i would say thats a good place to start if you don't want the saggy skin.. also and most importantly..DRINK A LOT OF Water. it will help replenish you and help with the elasticity.