Jacob, I've not seen any recommendations to wear a helmet in that area. While many people wear them in the steeper sections of the Mountaineers Route, the main trail is not as steep, and doesn't have the rocky sections above that might release some debris.
As for the shovel, it is up to you, but I would pass on the extra weight. There are a number of flat campsites, and some of them are sure to be flat enough for your tent. And campers before you will have leveled spots, too. But if you want to be absolutely sure...