It's not BAD to do the cardio on those days, but you will be interfering with the whole glycogen supercompensation aspect of the CKD, which is kinda the big benefit of a CKD.

As for a diet to contimue beyond a CKD, you can gradully add carbs back to your system once you have achieved your goals ...
I generally follow a diet designed by a buddy of mine called "Nutrition Know-how", which calls for alternating protein/fat meals (low carb) with carb meals. Many people have used it to great success, and I find it a great way to come "off" of a CKD.

But just slowly re-introducing carbs until you feel comfortable is a good way to go about it. It is another area that is highly individual, so you will have to find what works best for you.