Your original post was a bit confusing to read. You mention your sump failing, then change tack and start talking about replacing the refugium. I think you are using the terms sump and refugium interchangeably, and they are distinct and separate things. A refugium can be part of, and located within a sump, however. Not helpful to talk about replacing a sump when you are really wanting to replace a 'fuge, and vice versa.
You should have no issues replacing a sump with the display up and running. Take any macro algae you have and put it in a bucket of water. It will be fine for a couple days in there. Drain out your display until the water level is below the overflow level. Make sure you have some in-tank flow, and place a properly set heater in the tank on the inside front glass until you get your sump swapped out. You can keep your lighting schedule the same, unless it will heat the tank up too much, then either reduce or eliminate it for the time you will be swapping out the tank.
Remove all the water from the sump. Unplug and remove all equipment and hose connections from the sump. Pull the old sump, then put the new one in place, reconnect all equipment and you are done.
Not hard, really, just takes some time. Planning ahead with all holes drilled, all proper bulkheads in hand, and some new saltwater made up and ready to go all make the swap out go much smoother.
