firstly, copperbands don't eat nudis. fairy wrasses will never ever eat nudis too.
secondly, the problem with wrasses such as YW and sixline, is that they might not even do work.
the best approach is both biological and human intervention. biological, get some natural predators such as the above mentioned wrasse.
this might not be enough, so do some work on your part. coral RX is very effective in removing all pests, but the eggs are nightmare... eggs remain unaffected until they hatch and it will certainly be hell trying to rid all eggs from your tank. meanwhile, kill as many nudis as possible.