I have a red headed solar wrasse housed with a cleaner shrimp just fine. Placed 3 peppermint shrimp in the tank never to be seen again! Other fish are two clowns, scooter blenny, royal grame, and 2 coral cats. Did my wrasse eat them?
While possible he ate them, it is unlikely.Usually fairys will attack shrimp added to the tank while in the shrimp are still in the water column. Fairy wrasses are not well equipped to hunt a shrimp on the rocks.
Unless you have very sparse rockwork it is likely the peppermints are just hiding. They are very reclusive and can go unseen for months in a reef.