I don't know what to do. I started noticing my Scotts was eating like a pig, but seemed to be getting skinny. He was also scratching on rocks. Yesterday I picked up some Doctors G's food, but of course know he won't eat. He's just hanging out at the top of the tank almost vertically. I don't know what other information I can give, except he has no visible spots on him.
I've had two of them. The first one had a swim bladder issue and did this, it was too severe and he did not make it.
The second did this too exactly as you describe (although he ate better) and he recovered and is doing fine.
IMO I would run prazi to rid him of internal parasites and flukes. Ich doesn't seem to bother many wrasses, but it can affect fairy wrasses significantly more than others because they don't bury under the sand. However, the mucous coating they produce to sleep in helps keep the parasite at bay and wrasses are seemingly hardier against velvet and ich both.
That said, I would run prazi pro. Do some reading on it. It's reef safe I use in both of my reef tanks without issue. It can curb appetite, but my next advice should help. Also, take the cup off of your skimmer and let it overflow back in to the tank to keep O2 levels high. Skimmers will remove prazi if you leave the cup on.
Next, change what you feed. Wrasses LOVE Blackworms and live brine. I've never had any wrasse ever refuse BOTH of those for more than a week. I have 8 leopard wrasses that are notoriously difficult to get eating.
My wrasses go completely haywire for black worms. They're a fantastic nutritional food for all fish.
Also soak several mixed frozen foods in garlic guard or kent garlic, selcon, and cod liver oil. To do this, I mix a small cup full of 10 different types of frozen foods of all different types. I microwave it for 2 mins, and use a very small hole "strainer" from the grocer to drain out he nastiness and excess water so that the food can better absorb the above agents. Then, I mix it all back in that cup and refrigerate. I use it for 1-2 weeks depending on feeding frequency. You can also add pellets and some flakes.
This greatly varies your food offerings and a fish is sure to find something it likes. Don't do this with live black worms though, when they die (and they will in those ingredients) they foul up water VERY fast. Feed those sepearately. Same with live brine.