You can set up a small QT fairly easily -- it can be a tank, a rubbermaid tub, an old salt bucket... all you need is some sort of filter, heater, and clean water. Filter the water through a sponge or some floss, rubble, etc; anything that's been in the display or the sump that has been colonised with bacteria will keep ammonia in check along with water changes and Prime or AmQuel if needed.
If the wrasse is in the display with other fish, the only way I know of to actually cure the tank of ich is to empty it of fish -- ALL the fish -- get those fish into quarantine, treat them for 6-12 weeks, and leave the display fish-free during that time so the parasites will die off from lack of suitable hosts.
If you leave any fish in the display while you're treating the wrasse, he could re-contract ich the second you return him to the tank. Fish that show no sign of the parasite can be carrying it in their gills, and it will continue to go through its life cycle in the display; the second a free-swimming parasite locates any vulnerable fish, it's game on.
Ich sucks. Dealing with it is no fun, it's not an easy process, but watching fish slowly die is infinitely worse.