As you say, "no downside" to taking Ice Axe, but I doubt you will take it off you pack.
Is this a multi-day hike? Staring at Horseshoe Meadows and finishing at Whitney Portal? Langley, Muir, and Whitney along the way? This is a fairly popular "start/finish" route, but many variations as to how to get from point A to B. These peaks can also be done with two separate one day hikes, although they would be "big" one day hikes - especially if taken on consecutive days.
