I would lick the floor.
I know that sounds completely disgusting, but I think that I could find a teeny tiny remote spot on the floor that wasn't completely gross then I'd stick my tongue out and barely, barely, barely touch it to the floor. And that would be it.
But chewing other people's gum--that sickens me. There's just something about putting something in my mouth that has been chewed by someone else and has their saliva all over it...uck. And then add the whole stuck on the handrail with all those nasty, unwashed hands touching it. No thank you. (and haven't you read those reports that show that handrails are dirtier than toilets/bathrooms).
There you have it.
Our gross-out lesson is over. Thank you very much.