If your not opposed to snail mail...
I know that the military uses DHL mailing service with tracking in order to ship sensitive material. You could write down the code seal it in an envelope which you then hand sign across the seal. Place that envelope inside of another manila envelope which is not see through and seal all edges of this envelope with packaging tape. Do not have any distinguishing markings on this envelope. Place this package into DHL envelope. As for where this should be sent I would setup a trusted third party to act as a mail drop box between myself and the receiver. This might be a person or possibly another business which offers this type of service.
Face to face physical transfer of sensitive material is almost always the best way to exchange this sort of information if you want to ensure control over this information. (Although being present during the transfer presents other issues depending on whether your trying to hide your movements or if you are already under some kinds of surveillance.)
Setting up a direct communication line (cat 5, coax etc.) between yourself and the other party could allow you to send electronic information without being monitored.
As far as using a Diffie-Hellman, I think that is a great idea. Why not read the algorithm and write your own? this way you are sure that no one else is aware of the specific algo. you are using. http://en.wikipedia.org/wiki/Diffie%E2%80%93Hellman_key_exchange
Source: 9 years of military service and some naval security manuals which I forget the names of.