A higher incline should increase the intensity of your workout. At my old health club I always would see people walking at the steepest incline, yet holding on for dear life to the handle bars.
If you want to burn more calories, without increasing the pace, you can definately up the incline as your heart rate should increase.
Holding on, not swinging your arms, can be problematic for some. Basically 1) you never walk while holding onto something, so why get into the habit of doing so on a treadmill? 2) Swinging your arms helps keep the body in motion with the legs, and also the arm movements will help burn hopefully a few more calories.
I would recommend doing your best to keep the arms swinging and then eventually move on to running on a 0% grade, then gradually running/jogging uphill or even downhill.