First, get them used to being in their travel carriers NOW, give them their greens or pellets in there, and water of course. Then when the time comes, they will be comfortable in there and, it won’t be as stressful for them. Once moved you can let them keep the carriers as a safe place while they get used to the new house and, you can put them in the carriers, in as quiet a place as you have when the movers come.
You can’t let your life revolve around not upsetting your rabbits, they live in a home with you and need to get used to everything that goes on there, noise included. My house has loud noises at times, new rabbits are upset by it for a while but, they get used to it and learn to ignore it. That’s part of being a house rabbit, they have to get used to new sounds, scents, people, animals, etc… from time to time and, now and then they need to get used to a whole new house, no different than when you first got them.