One of my favourite fishes, the Yellow Wrasse...I've had 2 of them, first one in late 80s...
You CAN catch him to treat him after he goes to bed at night...that's how I had to catch mine

If you know where he sleeps, net the whole pocket of sand.....IF you need to get him...
If he's eating and otherwise behaving normally I wouldn't remove him from the tank. You can try some anti-bacterial flakes, if you think he's brewing something bacterial (cotton-mouth?) or if it's fungal (wait...isn't cotton-mouth fungal?)..hmmm not sure. It's hard to know without a picture....
At the very least, keep a close eye, make sure he's eating nutritious foods and perhaps use Selcon or other food soak to help boost his immune system. He might just be able to kick it on his own.
Contageous? Possibly, but if your other fish are strong and healthy, odds are they will not be affected. Sounds to me like something secondary after an injury...perhaps he got a wound on his mouth, and there's some bacterial or fungal thing going on. Unless another fish has a vulerability like a wound...they should be fine.
Hope this helps,
Jenn
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