I would be as quick as possible with the rock out of water. I returned to the hobby a few months ago by purchasing someone’s established tank that was getting out of the hobby. Decided to aquascape and the 2.5 hours the rock was out of water caused a mini-cycle.
I’m also working to rid some GHA. Was mostly contained to one rock. Got tired of removing it with needle noses and tweezers twice a week so started treating with peroxide. There is a long running thread about it here, I personally feel like I can’t comment on it yet as I’m not finished. I have two cemented structures and was unable to remove.
Regardless as you remove you’ll want to fix the reason for the algea to begin with simultaneously or it will most likely return