Get a shock cord and attach the pants to the rack. I put them on my back rack. Time and sun dries them, typically before the end of the day. In fact, I dry most of my clothes that way while on tour.
BTW. if it is less expensive, just purchase a chamois and wear it with shorts you may already own. Or buy a less expensive short, such as nylon athletic shorts. I am not aware of any advantages of wearing skin tight shorts on a tour where the goal is site seeing and not speed.