puffers, triggers and cleaners

Now before anyone gets irate, I do not have the above combination in my tank. What I'd like to know is will puffers/triggers or any other invert- unfriendly fish bother cleaner shrimp or larger snails (cowries)? I know hermit crabs and starfish are out for sure, just become a nice snack.
There's a very sweet looking huma huma trigger and I think it's an undulate puffer or dog face, can't remember the exact one here in the city reasonably priced and I would love to have one of them. Right now I have only a 4 line hawaiian wrasse and lemon damsel in my 80 tank.
 
It's definitely a puffer....the fish that is, not the name :) Unfortunately I'm suffering from a short term memory and can't get back down until tomorrow to see what sort of puffer it is.
I do know about the undulate triggers. I saw one being fed in a store and the darn thing ate a feeder goldfish in about.....hmm.... 1 second flat, just these little fins sticking out of the mouth. Cute..but I like my shrimp way too much to get rid of them.
 
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