I don't think a whole lot of people on this site are going to recommend that you use any kind of NO supplement, regardless of your diet or goals. Personally, I think that stuff is mostly gimmick, the money is better spent elsewhere. As far as cardio goes, jumping rope and shooting hoops should be ok.
You just have to remember that when doing a reduced-calorie diet, you should ideally keep your cardio low-intensity so as to metabolize as little muscle as possible. Also, a diet Coke here and there won't hurt, as long as it doesn't have calories or carbs in it. Diet soda isn't the best thing you can drink, but if a few of them are going to make the difference between sticking to the diet and falling off the wagon, then I say go for it.
Good luck. I think you'll find that the Velocity Diet, if done correctly, is a rewarding experience in a lot of ways.