Ok, I know you said you don't want to address him and embarrass him... but I see no other way! And he's a teenaged boy - sometimes teenaged boys need you to be direct!

"Hey, (insert name), I keep finding chewed gum outside my front door and I know you chew a lot. Are you chucking it on the ground? Please stop doing that and put it in the bin - it's gross and I'm worried that DS will pick it up and choke on it. I found a piece behind the couch on your last visit, I know you would never have thrown it there but DS must have carried it inside... lucky he didn't put it in his gob and choke. Thanks."