... his biggest challenge is the fact that he doesn’t perspire. .... Ironically, his disorder can make his hands too dry to stick to slopers and crimps. Rather than chalking up, he often resorts to misting his hands with water prior to climbing! http://www.rockandice.com/lates-news/tnb-super-unknown-austin-dark-horse-establishes-5-14d-in-random-texas-cave
I have climbed with someone who shares your issue, as well as climbing in locations that have very low humidity most of the time (i.e. under 20%). They climb with a small piece of damp chamois attached to the outside of their chalk bag, and periodically dampen their hands while climbing/chalking on routes. You may like to experiment with it.
Problem with super dry hands.