The particular specie of Caulerpa you say you have does not have a reputation for being invasive in reef tanks, so I'd expect that there are common grazers that will go after it. Foxface rabbitfish is one of the more likely candidates to graze Caulerpa IME. However, some Caulerpa are chemically well defended and IME there are some specie of Caulerpa a Foxface won't graze. Some Acanthurus tangs like A. japonica might also graze it. I've heard of some individual dwarf angels that will graze some types of Caulerpa, its probably more hit than miss though IMO. IME there is a low likelyhood that Tuxedo or Diadema urchins will graze Caulerpa, at least they didn't graze any of the three specie of Caulerpa in my tank. There are sea slugs that target siphonous green algae like Caulerpa and Bryopsis. There are even sea slugs that target specific specie of Caulerpa. I don't know much about them. I do know that Lettuce Sea Slugs do not actively graze for their whole adult life stage, and the ones I tried were not active grazers of Caulerpa or much of anything else, they just wandered around the tank until they disappeared. A sea hare might be a better choice, I've never tried one. As far as crabs, snails, or blennies; I really doubt any of these will graze any type of Caulerpa.
I dealt with Caulerpa peltata which is a very hard Caulerpa to get rid of by hand removal and attempts to limit its nutrient sources. But I never got rid of it altogether. And Caulerpas spread readily by fragmentation, so any little floating bit left behind after hand removal can allow it to pop up in a new place.
