I shower every day (sometimes multiple times a day if it is hot) but I only use clean water and fresh towel to scrub oils from skin and hair.
Once body adjusts it is possible to go longer time without shower with no problems. I did couple experiments but in the end I just like to feel fresh before bedtime so I stopped.
I can say it takes time for body to adjust oil production but now my hair is healthier than ever and I generally feel better.