Reef safe trigger?

I have a pair of 7 inch bluethroats in with all sorts of coral and fish no real problems they dont seem to eat any critters if fed. I have a lot of peppermint shrimp in the tank they hide well but if you would throw more in they would be eaten before finding a hiding place.
 
I have a Black Hawaiian Trigger that came out of a reef that was being taken down - housed with snails, but I don't recall any crabs or shrimp. I have him in a FOWLR and he doesn't try to rearrange the tank.
 
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