No you can't do combat zones without shooting, but nobody is forcing you to do combat zones. Just like nobody is forcing you to do combat zones in space.Can you do Combat Zones without shooting? Can hardly imagine that, however, you have now made me curious. I never did much of the on foot play yet (I'm out in the dark, but not quite under a stone) and all I know that it's basically one NPC team vs another NPC team, similar to the space CZs where you have to support your team in one way or the other - and if only by binding enemy forces which in principle doesn't necessarily require shooting.
CZs are just one of many things you can do in Odyssey, just like CZs are just one of many things you can do in the base game.
It's all about choice.