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I'd put them in a carrier with some of the old substrate and plenty tissue to bury down under. They will feel secure in the small space then you can put them back in to a fully cleaned cage. Some element of stress is inevitable and all animals need to exeprience a certain level of stress as a balance to keep the hormones correct. Wild animals experience stress every day in some way as do we.
When you return them you can sprinkle some of the old bedding on top to give some of the scent back and allow them to make their home again as they want it. I think they enjoy the digging and arranging to get it back how they like it myself.
With a territorial dwarf you need to be using a tube or box to get him out and then taking them away from the cage for taming and handling so make use of this time to do that.