That's going to be tough, since your super charges very slowly on its own, and you can only have 1 (out of 2) super abilities equipped, though you can swap between them once you have both. Killing enemies add a little boost, but if you're planning on not using a gun, it would be like a 5 minute wait or longer. You can melee, but you'd have to duck in and out of combat to let your shield recharge, and you can bet the enemies won't wait for you to get back to full. One of the main game mechanics is gunplay; Bungie designed Destiny around it and is including a lot of guns, some rare with special abilities, in this game. No matter what class you pick, you'd have to use a gun at some point because the wait time between supers is too great.