>>5761551000ft per mile is pretty doable. You might be a little gassed if you're out of shape, just give yourself plenty of time and drink lots of water.
Mountaineering is mostly about cardio. You do want to have some body strength, but there's no benefit really in being a big, muscled /fit/izen.
Most of the best mountaineers and climbers I know are scrawny little fuckers with a the resting heart rate of a corpse.