Speaking from my experience with a Nebulous Wrasse, they are an amazing Wrasse if you don't mind the aggressiveness towards other Wrasses.
I can't keep other wrasse with it, they will fight to the death.
It spends most of its time picking at rocks, eating any little hitchhiker it sees, it does eat snails and some clean up crews. I'd definitely expect it to pick off that cuc.
If you get them small and you have shrimps like cleaner shrimp...everything will be fine but one day when it's bigger.....he will most likely eat them.
I've never seen mine pick at any corals ever- they are considered "reef safe with caution" but I'd say so more because of inverts. For me, it was worth the risk, and it went my way which is awesome.
In the beginning it was the king of my reef until I started adding other fishes such as a hamlet which it holds its ground against but now sometimes swims away from. I added a Sailfin Desjardin and that became the king of the reef and the Nebulous slowly started realizing there are much bigger fish in its reef. It avoids problems now most of the time.
It also is a master at hiding for up to 2 months at times, especially when it's scared. It gets scared when you start doing tank stuff so it hides in the sand. Unless you know for a fact that you killed it somehow, never count it out. Mine has slept for ages then suddenly pops out of nowhere like nothing ever happened.
Anyways, this is my experience with a Nebulous Wrasse. It's definitely a favorite Wrasse, super cool.