In my opinion, a coral beauty is probably the least likely to go all NOM-NOM-NOM on your corals. I had one in the past with no problems and am looking to get another for my new tank. If you want a probability, I'd guess like 85.92% reef-safe (how do ya like that exactness?
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I'd put a Potter's Angel a little bit less safe than the coral beauty. Flame angels, I'd put at like 70% from the number of people that I talk to too.
From what I've seen and heard, they are less likely to nip if they are not crowded, under fed or allowed to establish their rank as "King of the tank". Nipping at corals though is a natural behavior and as much as you may try to prevent it they can always revert to it for no reason at all. I've talked to a number of people who've had CB's and Flames for years and years and one day they just start picking at corals for no reason at all.
Personally, I'd say go for it and just keep an eye on it. If it's a picker, back to the LFS it goes. I'd put money on it being totally fine in your tank.