so i reckon in the first phase she'd do it standing to copy Murdoc and 2D being nasty boys out in public. by the time Phase 2 starts she's taken up doing it in a more normal way since she's obtained a better grip on social norms, but in 3 it's right back to standing since she's traveling in a lot of places that don't have toilets, like on small boats and stuff. after that she more or less takes up standard urinating habits.

as an added bonus: i think Murdoc would probably have programmed Cyborg Noodle to piss standing up, though in her case it's not literally pissing but instead just expelling accumulated water vapor due to the general environment of Plastic Beach. i reckon she's relatively water resistant.