I would recommend setting up a couple buckets or plastic bin with salt water that is roughly the same salinity and temp as your current tank water that you can temporarily house the live rock in while you remove it. If you're going to have it in there for a while, I'd add a heater and powerhead to it as well. Also, make sure you don't have any inverts hanging on to your live rock as they will have a hard time adjusting to the new water in the bucket that you temporarily put the LR in. Not sure how to minimize stress on your fish, but hopefully someone else will chime in!
Also, there are a few threads in the fish section where people have made their own traps for difficult to catch fish, feed the fish with a turkey baster in the trap for a few days, and eventually the fish will become comfortable hanging out in it, then you can just drop the door when the damsel is hanging out in it and catch it that way. Might be worth a try if you haven't tried that method already.