Blue, what size tank? you may be ok if your tanks large enough. I have a 150 and most days they get along ok, the flasher steers pretty clear of the solar when hes in that mean mood and the solar makes him stay to one side of the tank., nothing serious, just alittle chasing, where before, it was almost constant. Most of the time they just ignore each other. And from all I have read, you can mix fairy wrasses.
I just love how the flasher flashes those fins. Mine has been schooling with my 2 anthias lately, eats well and seems very happy.