Will it hurt your mosquito fish or pond snails if you clean out your old dusty aquarium with dish soap while they are not in it?

It is OK to use a detergent when cleaning (scrubbing) out a dirty fish tank. The important thing is to make very sure the tank is scrubbed with clean water a couple of times after the detergent has been rinsed out. Any detergent left in the tank could easily kill your fish.