Trudee -
Having good ventilation in a darkroom is important - in the absence of fresh air, you will tire much more quickly, and the quality of the work you do will suffer.
That said, you don't need a system that creates gale-force wind. The key is air exchange - bring fresh air in, and let stale air leave. The metric is how frequently the system will exchange the air in the darkroom.
Assuming a standard 8' ceiling, your darkroom will have about 1730 cubic feet of volume. Suppose you use a system that has a rated flow of 300 cfm - that says that the air will be completely exchanged every 5.75 minutes - which is actually not too bad. Practically, a real installation will rarely achieve the rated flow, so a more realistic exchange time might be 10 minutes - and again, that's not too bad.
You didn't say what kind of work you plan to do in your darkroom. For conventional processing of film and paper (developer, stop, fix and wash), the fumes are not especially harmful to humans. Toning is the process that is most likely to introduce noxious fumes into the darkroom - selenium not especially bad, but some of the sulfur-based toners (sepia and brown) smell awful and the gasses they give off can fog unprocessed film and paper. My experience is that the risk of fogging is overstated, but it probably pays to be cautious.
You have raised the question of whether the ventilation system itself can be damaged by the darkroom fumes that it is exhausting. I think there may be two answers here - one answer is that the fumes can damage some of the components of the ventilation system (especially aluminum). The other answer is that the concentration of fumes needed to damage the ventilation system is so high that you would probably be asphyxiated before the equipment is harmed, and in reality the fumes will be so diluted by the volume of air in the darkroom that they are not going to do any damage.
But what that says is that the key to everything is getting fresh air into the darkroom.
My personal preference is for positive pressure because that approach helps manage dust better than a negative pressure system. However, it is often easier to install a negative pressure system.
In Hawaii, its probably not difficult to design your system to exhaust outside the building. That's always the best approach. In my darkroom, I have a blower that pressurizes the room, and I allow air to exit via an exhaust louver over the sink. If you choose to have both an impeller and an expeller (to use Roger's terms), note the subtle point he makes that flow rate of the impeller should be greater flow rate of the expeller to achieve positive pressure.
Final point - most "air conditioners" cool air within the room. For your darkroom, you want a system that will cool air that is brought in from outside the room.