Cupramine, is the the least toxic form of copper in the trade (that I'm aware of). The only species that I find do not tolerate treatments well, are any form of clownfish. I find they do fine for a short period of time, as in days, but experience health issues thereafter, often leading to death.
I treat wrasses the same, no matter the family. Even wrasses in the Halichoeres & Macropharyngodon, families. Many people, will tell you that a "sandbed" is required, this is not true. In reality, when first introduced into the aquaria, I highly suggest the contrary. I'm currently housing a female Macropharyngodon meleagris in QT, as we speak. Just recently, completed a 3 week QT in the same system w/ 2 Halichoeres iridis', with zero issues. They typically just lay flat, when sleeping. I can't tell you how many Macropharyngodon's, in the past, that I lost and introduced with a sand-bed. Most of which would bury themselves immediately, to never see them again. Understanding the fact that these specimens are shipped from all over the world and in different time zones, speaks for only one of the issues that come into play here. Where they could be used to sleeping during a certain period of day, may be the opposite of your photo period. To add, adding these fish to a tank without a sandbed, allows them the opportunity to witness food every single time it enters the tank and when the lights are on, they have no choice but to get used to your timezone & awake. One of my local fish stores mentioned to me one day of the difficulties they were having with these species of wrasses, stating that once they entered the aquarium (w/ sandbed), he almost never saw them again. I told him to introduce them into a bare-bottom tank and he said his success rate with these classes, had significantly increased. I can go on and on, about the logical reasons why you should not introduce these wrasses into an aquarium, right out of the ocean, with a sand-bed.
In reference to the QT process overall: I feel that it's an injustice not only to the fish, but our aquariums, to not QT & treat EVERY single fish (at minimum - fish) that enters our systems. Honestly, I personally believe it should be a requirement, for anyone in the hobby. After having the experiences in the hobby without a QT system and with one, I can personally make this statement. That's how much I believe in the process and necessity of it. We are risking not only large amounts of investments we put into the aquariums, but the livestock that is counting on you to care for them to best of current technologies, knowledge & sciences, permit/allow/support.