There are no shortages of bushes to pee behind on the PCN's in Singapore I don't ever recall having to have a shit when out for a ride by myself but I would probably just wheel the bike into the public toilet if that happened (same if I needed a pee in an area like ECP where peeing behind a bush may be deemed an outrage of modesty or whatever they call it) Alot of the time though I am mostly in a group so someone watches the bikes at all time.
I do a lot of solo riding and I think I suffer from mild IBS, so using the toilet while riding is a very real possiblity for me.
I've chosen to pick up a thick, branded cable lock instead of carrying around a heavy U-lock. I wouldn't trust ANY lock - even the most theft-proof - for more than 10 minutes.
Hence, the cable lock is IMO a decent compromise between weight and security. Anything longer than 10 minutes I would find a way to take the bike with me, and so far after over 7 mths of riding, I'm quite happy with it.