I have lots of pickers in my tank. If they are acting natural, then all angels will pick. All my tangs as well have learned to pick and some of them make a living out of mouthing slime off of the corals. Some like my Emperator Angel bite the ends off of the coral and the damage is odvious. Some like the Golden Angel and Golden Flake Angel do less odvious damage and the tangs and rabbit fish do no damage at all. But, they all pick and they all mouth the corals. If you fish dont do this its only because they havent learned to do it.
If the corals are healthy and there are enough of them compared to your fish load then they should be fine with the fish nipping and mouthing them. I think its actually good for them but... However, if you are not fine with it then yank the fish.