Fairy Wrasse can seem very finicky at first so be patient. Make sure no one is harrasing him. Other established wrasse, damsels, angels, etc. will really push their territorial rights on them in the first weeks.
So long as he is healthy and not threatened he should be eating a variety very soon.
It generally takes several smaller feedings per day to keep their weight up. I keep an auto feeder adding small feedings of flakes and pellets twice per day. When I'm home I hand feed the tank with the same at least two more times a day and with high-protein frozen foods, like Formula VHP, several times a week.
A school of Green Chromis help them feel safe to cruise the open water and teach them to eat ANYTHING. It's fun to watch the Fairys hang out with the Chromis school.
I have 3 fat, happy Fairys in my 120.