I think there is a reef safe trigger, which is smaller than most of its relatives. As far as sessile inverts go I don't think they bother, but I think any trigger would go for your crabs, snails, and shrimp.
As babies/juviniles the pinktale, crosshatch, bluechin, and sargassum triggers are all reefsafe ... when they get bigger they may eat shrimp and other inverts but i'm sure if you keep them fed well they will be ok. And if you get them small it would take a while before they got to be large.
My crosshatch doesn't bother any other fish at all, but he has knocked off one cleaner shrimp. I guess she couldn't resist it. Other than that she is very well behaved.