You CAN do high volume training when cutting, and if you're used to such intense training and the volume, then there is no reason why you can't follow either training programme.
If you NOT used to training with that much volume or intensity, then no, I wouldn't recommend it and get you to reconsider.
Fat loss does not require you to drastically reduce calories or carbohydrates and be stupid with your nutrition in order to get results, and the more active you are, the more you can eat and still lose fat! I hate that word "diet" - diet should be LIFESTYLE NUTRITION that you adapt for your goals, not a short-term process as a means to an end.
As far as cardio, it's not necessary for fat loss, but you can add it. Just make sure you are eating enough. You can do high intensity or low intensity - whatever is personal preference and most convenient, really, although shorter, high intensity sessions are the best for fat loss, IMO.