I've only treated a few wrasses in copper and never had an issue so that matches my experience. Might want to at least consider updating this sticky.
Fish and Treatment Guidelines (with chart) The following chart is a quick reference guide on what QT protocol should be used according to which type of fish you are running through QT. It will give you an idea of which methods are generally safest with certain species but is not meant to be...
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"** Wrasse in general should be allowed to settle and start eating for several days before copper treatment is started. While they can handle copper, it’s best to give them the time before hand for maximum chance of survival. If a wrasse has an injury or infection before going into QT, that “settling time” should be extended until the injury or infection has healed completely before starting copper. "