Radiant wrasse if your tank has a lid, though they can be hard to find healthy and are relatively pricey. Once established and eating they're very easy to keep. Might go after shrimp and the occasional snail but 100% coral and fish safe, very active, shouldn't be aggressive either.
If not, the royal grammar is the best option I've seen mentioned, they're active enough and very pretty, and not completely purple.
One thing worth mentioning - purple will become a very common color in a reef tank due to coraline algae...given the choice between a purple fish and a fish that is not the color of an easy to keep coral, algae, or lighting (so...yellow, orange, and red to some extent) I'll take the yellow or orange fish (or fish with one of those colors...the aforementioned wrasse, purple tang, royal gramma) 10 times out of 10.