"¿Por qué no quieres ducharte?"
Translation:Why don't you want to shower?
I might say Do you fancy a drink? or Do you fancy seeing [a movie]? but I can't imagine saying Do you fancy a shower? and certainly not Why don't you fancy a shower?
Ducharse suggests you are asking ustede the question; ducharte implies tú. Would you more likely ask this formally or informally? Probably informally.