It doesn't rain too much in August, so I think it's safe to go on those dates. Just to be careful, why dont you keep a tab on the weather conditions in Manali on 9th and 10th.
Please do not worry about the drive, Roads are wide and good.Rain would not be problem for you , I am sure you would love the drive from Kulu to Manali.
Mostly the road from Delhi to Manali is quite good all the way upto it.. Only concern could be of landslides during rain but generally the area is cordoned off during rains and could lead to some delay but nonetheless pretty much safe to go by road