Every fish is susceptible to ick. Tangs just have a bad track record with it because they stress more easily than others meaning their immune system is lowered. With an immune system that is running as well as it can, it invites diseases and parasites to attack or show themselves. With proper QT there is no reason why any fish, even tangs, should get ick unless you skipped QT for your first addition which is a really bad ideas. An ounce of prevention will go a very long way in this hobby. Trust me there is no way you can keep your fish long term with ick because it is simply a ticking time bomb waiting to blow.
Now to the OP. Like others have said, there is no tang that will work out in your tank. I would suggest looking at dwarf angels. The most reef safe ones are flame and coral beauty angels. If you start a thread for info on them there are plenty of people, Todd especially, who could help you decide if you can't.