Do you wash your hands after applying skin products and before doing your hair? {Your Opinion}

I like to keep my hands clean all the time. And, whenever I apply any moisturiser or sunscreen, I like to wash my hands afterwards. That's also a reason why I don't like hand creams because they tend to make my palms sticky. And, also, before doing my hair, I like to wash my hands so that the skin products don't get transferred to my hair and make it greasy or create a product build-up.

How do you manage your skin and hair care routine? Do you do your hair before your skin???