I would be very careful about doing strenuous exercise whilst on a Vlcd. We are on literally the bare minimum to keep us healthy-ish and alive, if you start adding exercise to the mix your body simply does not have the fuel (cals) to support the extra you are asking of it by doing the exercise. Our bodies are then at risk of breaking down muscle to fuel us, bearing in mind our heart is a muscle.
Saggy skin is a worry for anyone

but exercise will not actually make to much of a difference to the likelihood of us getting it I'm afraid

It's like a person relentlessly doing 400 sit ups every day to "tone" up loose tummy skin or to loose bulk (fat) there when in fact what happens is the muscles of the tummy underneath the skin come to be in fantastic shape but the skin/ fat has minimal change.
I am a great believer in exercise, a couple of years ago I was eating healthy and exercising and my body shape was completely different to what it is now at the weight I am at now I was actually smaller then now due to the exercise leaning me out but that's the price I pay for wanting the faster losses now.
Skin can take up to 12-18 months to catch up with rapid weight loss. Lots of water and a nice skin care routine can also help things and usually we build it up to a far worse thing in our heads then it actually turns out to be.
Wow sorry for the ramble, I blame the black coffee making me go ten to the dozen lol!