Keep in mind that grease isn't natural though. Crude oil is natural, and we get cosmetic grade petroleum/petrolatum after crude oil has been processed, refined,filtered, had things extracted, had things blended, etc. to then be used in cosmetics.
There's nothing wrong with grease though. I personally would just use a regular shampoo along with it though, because it will build-up on your scalp over time if isn't being washed out. A mud wash would not really be enough.
Is there a reason why you want to switch to "all natural" options? If whatever you're doing now is working, don't feel like it's inferior to things marketed as "natural". That word isn't regulated, so anyone can put a green leaf on a product and call it natural while it being everything but. Pretty much anything can be marketed to appear good or bad, try not to get caught up in the hype.
This cracks me up every time