There is no reason to move your corals unless he setles in a spot right next to a coral for any prolonged period of time. Coral will recess until it has gone by. It is the long term exposure that will kill a coral. My anemones have moved from time to time, rolling all over the corals, they simply recede then open up again.
If you own an anemone, that is a risk you should be willing to take that it might find a home in the middle of some shrooms. You willl have to move them if he stays. You should have all powerheads and strong intakes covered with a sponge as that seems to be number 1 cause of anemone death next to it being in a new tank or bad parameters.