I wound up sporting the shirt. First of all, temps were lower than forecast so between most of the climb being in the shade and a breeze to help me keep cool, I figured that swamping out my shirt wouldn't be such a big problem.

More importantly, most of the people where I work are women. Those unable to resist the eye candy might throw themselves uncontrollably at me which would create a hazard. I climbed the hill without incident, washed up in the restroom, and quickly dried my shirt with my office fan.