I WOULD reverse this. The first day (which, due to altitude will be the toughest), will be much harder if you go over NAP. Something like 1,500 feet of extra elevation gain, and it is almost 10 miles to lower soldier, compared to about 9 via cottonwood pass.
I WOULD base at lower Soldier and dayhike to Sky-Blue. the camping in not so nice at that lake-rocky. Alternatively, about 3/4 mile below in the Basin, there is a grove of trees below the Miter. Back to Soldier, or relocate to Upper Soldier, and next day climb up to the Langley Plateau trail from there, as some like to do. A bit of a slog, but 3/4 mi, 1K gain, but gradual. It does save 2 miles.
