"He doesn't bathe because of the water shortage."

Translation: Kvůli nedostatku vody se nemyje.

[PetrLongin]

I think the translation is not correct.
"He doesn't bathe." - "On se nekoupe." For example. He does not use a bath, but washes his hands.
"He doesn't wash." - "On se nemyje." He doesn't wash at all.

[VladaFu]

What you propose is not used in English that much. Definitely not as the default.