I think the fairies are a great group of wrasses in general. I love watching my male Lubbocki display in the evening. Then he'll go chase the female. He's very impressed with himself. Doesn't notice other fish at all, except for the female Lubbocki. I'm not sure on fairy wrasses' pest-eliminating abilities - they may help, may not, just don't know.
I do know that, other than the sixline, the yellow "Coris" (Haliocheres Chrysus) is a good bet for eating unwanted flatworms and nudibranches. I have a pair of these also - the bigger one went terminal phase after I added a little bitty one. It was cool - at first the big one was very shy, a little psychotic, always fleeing under a rock whenever somebody entered the room. After he turned into a male he became much bolder, flitting around with his fins outstretched, displaying for the female. He doesn't notice any of the other fish at all.
If you want a fish similar to the "yellow Coris"/Haliocheres Chrysus, and if you are willing to pay $75 per fish (if you're lucky), then I would suggest Haliocheres Iridis. They're hot. Same general behavior and pest-eating abilities as the yellow wrasse.