Leah-
Great to hear from you. I imagine that there are a number of such organizations in NYC. Off the top of my head, you might try Global Goods partners:
http://www.globalgoodspartners.org/template/contact.cfm
They are sort of "fair trade middlemen", at least in principle, though I don't know very much about their specific practices (and/or how fair their trade is really). You might have luck just searching "Fair trade nonprofit new york" in google.
I'd love to discuss your project in more detail. Why don't you send me an email at my office -- dmuren(at)u.washington.edu -- and we can set up a phone call or iChat.