Is it a bad idea to run RJ45 cables through AC duct work?
I would avoid this as much as you can. It is not professional to use existing AC ducts for cable (they are not designed for that). Besides the previous points of non-plenum cable killing everyone with toxic smoke (before you even escape the fire) you just don’t want to do it. I’d suggest wireless if that’s an option or fishing the wire through the walls if you can. If you can’t or don’t want to do this hire yourself a contractor to run some cable for you. It won’t be cheap, but you’ll get a nice job (if it’s a good contrator) and some quality wiring. It will probably be cheaper to run wireless.