There’s shampoos that are safer for animals, it’s not unheard of to wash animals but completely unnecessary based on what you’re describing. So long as you don’t do it too often or cause undue stress, it’s your time and money so go for it.

Alternatively, you could provide them with specific dust to bath in that won’t discolor them. You can mix herbs and perfumed things in to the dust which can even have some health benefits.