The only solution is to get up and go. The quickest way is to sit up feet dangling in the HH slot, step into your boots, take a step or two to the side and go.
"Uh Skipper, I gotta go pee."
The tube idea isn't so daft.
There was a thread about an English Channel crossing on the Song of the Paddle forum where they discussed peeing mid way across.
There's a kind of external catheter, sounds something like a condom with a tube on the end. Whether you'd use it to just go over the side (err, no) or get a good aim into a bottle I dunno.
Could be worth looking into though.
"Uh Skipper, I gotta go pee."