All the research I have seen indicates that CDK and other low/no carb diets are no more effective than any other diets. They do not spare more muscle than other diets, and they will leave you will less endurance energy. I personally think it sucks to be on these types of diets. I really don’t understand their popularity. Unless you're already at a very low BF%, then I see no advantage to CDK type diets. By far the most important part of any diet is calories in vs. calories out. The micronutrient ratios are far less important. There is no rule that says you can't lose fat without cutting out carbs. Many people cut on high-carb low-fat diets. Cut your calories by about 500 cals/day below maintenance, and you'll start dropping fat at a safe and steady rate. Also, make sure you are including some relatively heavy (weight wise, not volume wise) resistance training to help preserve muscle tissue.
Good luck to you, I hope this helps!