I would look for the cause before jumping in the car and running to the LFS for a fish you may not need, and that may unnecessarily increase the bioload of your tank and then further put your inhabitants under horrible stress. My opinion, find the cause then decide whether a new tank mate is needed to fix the problem. Not only that, wrasses won't totally eradicate a problem bug they will only keep it under control and that is hopeful too. Eggs hatch at a great rate will eventually cause more problems even though a wrasse is in the tank, but that is if it truly is a nudi problem to begin with. Take a look at night over the next few days and then you will be sure if it is another inhabitant or not.
thanks,
Rick