PRIME,
It sounds like your pool room is quite large and that you would like to utilize it in the winter but cannot until it is properly heated.
Depending on how large the one duct you had planned on moving is (6",8",etc), you may not have enough heated air supplied to the pool room to be comfortable enough to use it in the winter. As far as damaging you HVAC system with chlorine, it also depends on whether or not a return air duct will be added to the pool room. The chlorine should really only damage the duct and not your HVAC system if no return air duct is added.
Another thing to think about is whether or not you new furnace is properly sized for the pool room. If it was designed and installed for you home only and not the additional heat the pool room would require then it could have adverse effects the rest of your home's heating.
Depending on the anwsers to the above, I would suggest looking at a seperate system for just the pool room. I would possibly look into a ductless split system heat pump system. Mitsubishi makes a system called the "Mr. Slim" that would probably work well with you current situation. You can find more information on their website
http://www.mrslim.com.
The ductless system requires no ductwork and provides both heating and air conditioning. This allows the temperature of the pool room to be controlled all year round, plus you won't have to actual heat or cool the room unless you want to use it.
If you change your current system's ductwork, you'll be heating and cooling the pool room regardless of whether or not you're actually using it.
Hope this helps.