I don't like not being able to shower, but I have stayed like a week without showering in the past, because my grandparents don't have any shower or hot water or even toilet in the house X_x. I would choose being able to shower and wearing the same clothes for a week though. Way easier to do.
I'd pick shower for a week, last summer the water stopped working in our house for 3 weeks so, I've experienced this. However, I did take sponge baths and use baby wipes which is kind of "cheating". Overall, it made me appreciate running water so much more.
I'm not sure if it would make a difference either way though because with wearing the same clothes everyday plus showering, you'd still stink.
Not shower for a week. I mean I break the record myself without even trying I hate shower. I don't shower for so far 3 weeks already! And no I don't smell bad. I think shower is a waste of time and energy and shower gel and lotion.