It looks like there's going to be a lot of people up Skyline next Saturday.
http://www.mtsanjacinto.info/viewtopic.php?t=3526If you can get to the tram, you'll be fine for Whitney. If you can do the whole Cactus to the Clouds, you'll be golden for Whitney. If you can breeze up there, you'll have no problem with your sub-10 hour time.
Be VERY CAREFUL with Skyline!!! It's getting hot, and people have died coming down after giving up due to heat strokes. I'd carry at least a gallon of water if I was you. Read about the hike carefully before attempting. Good luck.