If this were my bag, I would give it a bath. As someone previously mentioned, there is no perfect technique, and there are no guarantees of how it will come out. If you are a novice at rehabbing and are concerned, practice on some other bags first. I've tried various soaps, and I prefer to use Woolite for my rehabs. There are lots of choices to try to get the marks off, but there is no guarantee they will get better.
A bath is not really going to shrink the leather, but you can reshape it back to its original shape as it dries. After the bath, stuff the bag with towels and reshape it. Stuffing a bag is not as easy as it sounds. When I first started, I was overstuffing my bags. I'm now much more careful about not overstuffing. I also roll towels into logs. I tend to like using thin towels as well.