Peppermint shrimp are reef safe. They are not known for eating other inverts but of course each one is an individual. Still, I've never heard of it happening.
Now, biological controls have ups and downs. While many people swear by these shrimp, not every peppermint shrimp will eat aitpasia. Period. Some that have eaten them in the past will stop, and vice versa. The berghia nudibranch is an obligate aitpasia eater. As in it can not eat anything else. They will eat every last bit of aitpasia and leave nothing, not even a single cell behind. But then they starve so its best to pass them on to another hobbyist.
Boiling water, lemon juice, kalkwasser, aiptasia x, etc are all tried and true means of removing a few at a time and if you only see one or two that is the way to go. If you can remove the rock, you can burn the anemone off with a lighter.
If you go the shrimp route, odds are good that they will control the aiptasia to the point that you'll never see another one. But there is no guarantee of that. Also, some of them are sloppy and won't eat every last bit of the foot. There are tales of introducing shrimp to eat one or two and when the shrimp eventually die or are removed, aiptasia pops up all over.
Not saying this'll happen to you, it's just important to recognize that biological controls are not foolproof. My cat is a terrible hunter and I wouldn't use her to attack mice in my house.
Whichever route you go, good luck!