I don’t believe Reb Moshe would approve of his words being used in this instance. HE said it was preferable to give your business card in lieu of shaking a woman’s hand. He didn’t suggest that You walk around handing your business cards to women!!!!!! So please don’t twist his words to serve your purpose or to defend your position it just doesn’t hold water.
I am a woman and I don’t like the sevivah in Manhattan so I choose to go there as little as possible. I drive rather than take the train as much as possible so I have choices and so do you. And if I thought a man dressed improperly because his pants were too tight and nothing was left to the imagination, or his underwear was showing I certainly would not hand HIM a card that said “dress modestly”! It would not be MY business to approach any male. So looking at it from a male/female female/male perspective I hold firm and stand firm in by belief that it is not your place or any man’s place to look, approach, speak to or hand women anything especially when they are not dressed appropriately or have any business involving your family or parnasah.