A regular nurse handles urinal placement for penises and does pubic shaving for surgery, you know.
Literal
Normal nurse [topic-は], penis [to-に] urinal [also-も] apply [and-し] surgery [possessive-の] time [topic-は] pubic-shaving [also-も] do [emphasis-ぞ].
Blunt medical/anatomical content. ちんこ is vulgar slang for penis. 溲瓶 (しびん, 'urinal/bed pan') is medical equipment vocabulary. 剃毛 (ていもう, 'shaving body hair') is a clinical term for pre-surgical preparation. The し listing ('does X and also Y') chains tasks. ぞ is the masculine assertive sentence-ender. The speaker is matter-of-factly countering someone's squeamishness about nursing duties.