You can add genicanthus angels to your existing reef. They are open water feeders and will leave all your corals alone.
If your tank is well established and mature you can add a variety of the dwarf angels. Most of them really like to hunt for food amoung the corals and while may occasionally nip at a coral won't actually devour a coral.
I've had Goldflake angels in my reef tanks with all sorts of corals for the last 10 years without any major issues.
If you are looking at the larger angels - Imperator, Koran, Chrysurus, Cortez, Navarchus - Then a second tank would be a safer option. I had a 6x2x30" tank with a large collection of tangs and angels for many years.
Dave B