There is a dog park near my house complete with a hose for keeping dogs from humping each other while off the leash. I'm sure that your company has professional conduct rules that are intended to act as the hose.

What you can do is have COMPANY business cards printed with your contact info. Write a personal note on the back thanking a customer for their business and give them to say, all first class passengers.

If there is any interest from the hotties, they'll have your number. Otherwise you've just performed some marketing that may get a customer back on your jet. Either way you don't look like a creep.