Moving your liverock around is not such a big deal, you might find that your coraline aglea might grow a little differently depending on how you move it.
My concern would be if your liverock is imbeded in a DSB. Then moving your rock might cause a problem if you are pulling it out of the sand.
In moving it out of the water you should keep a rubbermaid tote or 5 gallon bucket(s). Turn your system off and syphon some of the water into your container(s) and place the rock in them for temporary time to keep them wet.
Thomas