I was wondering if there is any service where I can
send my mail to get it postmarked in a different place,
so the receiver does not know who/where it came from.

The specifics:
I wish to send some damaging emails to an executive at
the company I work for- basically whistleblowing, and
I do not want them to be able to prove it was me.

If I knew someone in the area of the other plant, 
I would fedex to them and let them drop in the mail.

Anywhere between Chicago and Milwaukee to get my 
mail postmarked would do.  

Thanks

I am assuming that you want to send this letter through the USPS.

Place the letter to the executive (with proper postage and addressing)
into another envelope addressed to the postmaster of the post office
of your choice. When the postmaster of that post office recieves your
letter, s/he will open the letter addressed to him, and see the letter
addressed to the executive. The letter to the executive will then be
postmarked and sent on its way.

http://www.celebratelove.com/valpostmark.htm

Depending on the situation, the above postmarks may be fun to use!

Hope this helps,

Joe