I would consider it safe to do solo, if you're a strong hiker. You're backpacking, so I imagine you're spending the night somewhere on the trail? That'll make it easier, splitting the ascent into multiple days. I wouldn't bother with a guide for the Mountaineer's Route, especially in Aug/Sept. I did it last October as a day hike (TR here:
http://www.whitneyzone.com/wz/ubbthreads.php/topics/40720/Oct_18_Mountaineer%27s_Route_Rep#Post40720). There were other people on the trail, and campers at UBSL.
