Your chickens will not hate you if you give them a bath, wildlife rescuers use a dish washing liquid like Dawn, if you have that in New Zealand. I suspect you do but any brand should work. But I agree with Wyorp, it is not necessary. I don't know how cold it is where you are but I would not want to give them a chill.
Dried dirt will not hurt them. Eventually it will come off. Rain would be a natural cleaner. They may just fluff up their feathers and shake if it bothers them, sending up a cloud of dust. If they have access to dry dirt, they may take a dust bath. Sounds strange, using dirt as in dust to remove dirt. This is one I think you are probably better off not trying to fix a problem that really isn't a problem.