I'd suggest doing what mattzang has said. To be honest I very much doubt you'll catch him. These fish are not stupid lol. I have one in my nano, 2 Anthias bigger than him, and a 6 line wrasse the same size.
He was harrasing the six Line for 4 days non stop when I decided to remove him. Well let me tell you he had other ideas.
I spent 3 days trying. Left a net in the tank overnight to let him get used to it. Soon as that net moved he was gone. I spent 45 min holding that net still, he would not come out from the rocks. I go toilet come back he's there staring at me ready for round 2[emoji35]. The six Line Wrasse however was more than happy to get in the net. Almost asking to leave. So that's the option I took. Set up a small 5g temp tank for the wrasse. He's not very happy which is more than can be said for the Anthias who are now on his hit list [emoji85].
So long story short, drain the tank and get it done. Don't worry about your water chemistry an so forth. Do as advised and keep the rocks wet, don't touch the filter media and it'll all be fine.
How you get the fire fish out the rock is another story. But maybe you will catch the dottyback before removing that particular rock. [emoji6].
Good luck. But don't wait around. That firefish won't last a few days I bet.