Believe it or not, this is a semi-serious question... I was visiting a great shop that had some vintage brands of men's cologne and had a sniff of Caswell-Massey's "Tricorn" that was favored by John Barrymore and Cole Porter. It's a really nice warm sandalwood scent right out of the past that doesn't smell at all like the nasty drugstore colognes of today. So, did Jack have a signature fragrance?
Of course, Fred Allen style ripostes to my super-esoteric question are welcome as well...
I think there were a few radio gags about Jack wearing "My Sin" (a then-popular woman's perfume), now that I think of it.