Do you have the scientific name of the fairy wrasse you are talking about?
Do you have a refugium? How old is the tank? I wouldn't get a mandarin until the tank is at least a year old, otherwise there is no way the tank would be able to sustain just a mandarin. Mandarins can decimate a pod population fairly quickly with nearly constant hunting and eating all day, working towards training it to eat prepared foods would be a good idea to help out. Wrasses, undoubtedly can out compete a mandarin for pods, which could present a problem. Fairy and flasher wrasses don't compete as much as other wrasses do IMO, so you could be fine depending on the answers to the questions I asked.