Check if there are any other symptoms (i.e. mucus, sneezing, etc) involved with the wet nose. Check the paws also for signs of mucus. Also, observe his behavior. Does he simply have a wet nose? Or is it accompanied by other symptoms (change in stool or appetite, lethargy, etc)?
In any case, I would recommend taking him to a rabbit savvy vet. Even if the wet nose turns out to be normal, at least you’ll know what a healthy and unhealthy nose looks like.
My baby bun had a runny nose along with sneezing. I adopted him at 8 weeks, and a week later, he developed a runny nose along with sneezing. I took him to a vet immediately and had a culture test performed. The culture test confirmed Bordetella, which is supposedly treatable with antibiotics. He’s still on the antibiotics treatment (3-weeks treatment), and I’m waiting to see if the medication will eradicate the infection. Otherwise, my baby bun is happy and active. It’s just the runny nose and sneezing that bothers him sometimes.
Good luck!