When you’re out and about for the day, you can’t get picky about where you do your business. Your options are: a) try to hold it until you get back to your hotel, b) find a restaurant that will let you use their facilities, c) use a public toilet, or d) drop a deuce on the sidewalk and hope your friend picks it up in some newspaper and throws it out. My advice is to spend some spare change, hold your nose and use the public toilet. It may be soaking wet, but that’s probably from the self-cleaner.
Note: Your friends have every right to shun you for the remainder of the day once you emerge from the public toilet. It is fair to assume that you are now a biohazard. But at least you didn’t poop your pants.