I had the same thing on my 94 K1500 with a/c. Instead of ripping the dash apart, I cut the lt green/black wire running to the blend door actuator. Of course the recirculation for MAX AC will no longer work, but that I can live with in my quite truck cab.
Here is a pick with the glove box out and the wire I cut. Its poking out of the harness with the fresh electrical tape.
Peace,
JC