What is the problem exactly with an SMTP server ? Is this that he don't want
an SMTP server at all or could it be just installed as a relay to the main
mail server ?
If he don't want an SMTP server at all, you could perhaps use a shared
location on the mail server (AFAIK if you create files in the appropriate
directory they are picked by the SMTP mail server) or perhaps call somekind
of process on this server (either using a web page, a web service, a DB,
remoting or whatever else is allowed) to send this mail directly from the
mail server.
A key point would be likely to understand what is the exact point that he
dislike (I'm not an admin but AFAIK a SMTP server is not evil in itself, the
problem is how well or bad it is configured).
The last resort would be to log all this let's say in a file or a log and
have something that delivers these files to you (using a network share or an
event log reporting tool ?)...
Good luck.
