Have some whey and some carbs before you run if you don't want to loose muscle (who does?), in the morning when you wake up you're on catabolic mode, you body is not
building muscle it's destroing it, unless you eat something right after you wake up it will only get worse, and if you add cardio (wich helps you to loose muscle) to that your are really asking to have negative results regarding muscle gains, you'll get smaller and weaker.
Eating as you wake up actually increases your metabolism and tells your body that it's ok to burn fat, the longer you stay without food the more your body will try to save your fat, and it'll use your muscles as a source of energy, now you don't have to eat a lot, just about 15 to 25 grams of whey with just about the same amount of carbs will do the job, and it's also very important to eat right after your workout.
You have to look at the big picture, you have take the amount of calories that you need (according to what your goals are) and split it into at least 5 meals throughout the day to maximise
fat loss. You'll burm more fat by the end of the day by doing that.