Only my own thoughts here so take it as you like it.
I'm a big believer in training correctly and training for what you are doing. If you are running to get better at running (triathlon), you should be using correct technique. No shoulder shrugging (fight stance), using arms in time and opposite to legs, as little upper body movement as possible, etc.
If you are running to improve your cardio for a fight, think of it this way. Are you going to run in the cage? No. So there is no need to run in a fighting stance, it's just an inefficient way to run. It may actually cause damage or unnessecary strain on muscles and joints because of this (obviously without actual visuals and study you can't say). What you are wanting, I'm guessing, is improved lung capacity, stroke volume, lactate threshold, etc. Which you will get (and with faster results) if you just focus on the running without the awkward additions on top. Weights are cool though, if it doesn't impede your technique. Light ankle weights would be worth a try aswell as, or instead of, the light dumbells.
PS - Good with the core. Transversus Abdominis ftw.
