I don't want to rain on your trip, but... Mt Whitney is a pretty rough trail for ski touring. There will be a few sections where skis would be ok, but then the major climb up to Trail Crest is so steep that people use crampons and ice axe to climb. Going down would be challenging at best for experienced telemark skiers. By that time in May, the freeze/thaw cycles will likely have a really icy crust when cold, and then slushy when warm.
Mt Whitney is not used by x-c skiers hardly at all. I've seldom heard of anyone going that way. Only truly experienced back-country x-c skiers would try Whitney.
