I exercise whilst on CD but the key is to keep it fairly light - we just aren't taking in sufficient carbs for heavy cardio workouts.
I use the treadmill (brisk walking), bikes and rowers all on a medium setting and only for 5 or 10 mins at a time ... then a couple of weights machines then back on a cardio machine for another 5 mins etc until I work my way around the gym (takes about 45 mins).
Swimming, cycling and walking are all good but again, keep things easy ... enough to get you 'warm' without lashing sweat.
Definitely DON'T do any exercise running empty: I made the mistake of going to the gym just before I was due a pack and I was totally wiped out afterwards. I felt dizzy, weak and when I got home I collapsed on the sofa and slept for half an hour.
You could have half a pack 15 mins before If you wanted to save some for later but give your body a bit of fuel to work on.