I lived in SE Alaska for 14 years and had a shop there. It is a rain forest - always wet and cold. I ran a dehumidifier most of the year and it seemed to manage the humidity pretty well. I had the occasional rust spot from a spill, but I don't think that I ever had condensation while it was running.
Someone said it above, but the propane combustion is going to release H2O into the air. I would get a different heat source, or get a radiant tube heater fired with propane that is vented outdoors. You'll always fight condensation with that type of heater in there.
Man advances just in proportion that he mingles thought with his labor. - Ingersoll