There are many weary and well-trodden euphamisms for this but do you know of a more obscure one, maybe only used by one person you know? For example, my grandmother would go to "shed a tear for Nelson".
The saying is, 'I've got the turtle's head', which means you need to go. Another is 'I'm touching cloth'.
I've also heard 'I'm off to lay a bag of turf,'. And once someone shouted through the toilet door, 'Hurry up - nip it short.'
Some people can be so crass.