I'm not the best guide for how often to shower, but every dermatologist-written guide I've read does indicate that a daily shower is unnecessary for most people and will (for most people) dry your skin. It can also damage your hair. This is true even in the absence of soap/detergent/shampoo.

That said, if you do anything that causes you to sweat, I think it's prudent to do a quick rinse because you always smell worse to other people than you do to yourself due to olfactory saturation.