Suppressing message-id generation locally

[Harry Putnam <reader@newsguy.com>]

Following along with the sender header discussion I decided I should
disable message-id generation on my end and let the posting host for
news or smtp (outgoing) for mail set it.

Kai suggested:
  (setq message-required-news-headers (delete 'Message-ID
  message-required-news-headers))

Which does the job for news, but what about mail?

I thought maybe a similar thing like this:
   (setq message-required-mail-headers (delete 'Message-ID
   message-required-mail-headers))

Which does stop gnus from generating the id but it still gets
generated locally (and incorrectly) like below:
        <200105261236.f4QCaU927207@reader.local.lan>

So how to proceed, if one wanted to disable message-id at the local
MTA level so that my local MTA (sendmail-8.11.2-14) passes the message
to outgoing mail machine at ISP (where I have no say in config) with
out a message-id, so that regardless of MUA the message id would get
generated at the outgoing smtp machine.

I'd like the mail handling software to deal with this, without my
having to force a correct message-id.  But not so clear how to do
that.  I'm behind my own firewall, on a locally named/addressed
machine in 192.168 range with no (internet recognized) FQDN.

My firewall, a NETGEAR FR314 DSL/router holds my static IP address but
does not process mail, beyond passing it through.  I can think of
several ways to kludge this so it comes out right but wanted to follow
`Rats' advice and let the mail handling software and network settings
deal with it, and get it right.