My husband said that he didn't wash his hair for months on end when he was in Australia. It took about a week to 10 days for it to look good without washing. One week back in London, and it looked gross and grimy very quickly. He is convinced that the no wash thing can only work well if you are in a "clean" rural setting as the natural oils, etc can only overcome regular "dirt" and not the soot and grime that you have in a city.
My hair is long, thick and wavy. I wet it every time I shower, which is often as 2 or 3 times a day. I only towel dry, don't blow dry, and don't use any styling products. I wash it about once or twice a week, or if it warrants it, i.e. been sat round a bonfire, at a curry restaurant, baby upended spaghetti sauce into it.
I don't use a shower cap, I don't use dry shampoos. People compliment my hair all the time and say that it is lovely and enviable. I think I'm just lucky.
Good luck to you and yours,
F. B.