If you have enabled Word to be the editor of Outlook 2003 E-mail messages, you may have "lost" a common Outlook function. You appear to lose the toolbar icon to add/delete/change signatures in an e-mail message. Here's the alternate process to add a signature to a message.
In Outlook 2003, create a new signature, but put nothing in it - no text at all. Name it something obvious - "empty" or "blank" etc.
Now, when creating a new message, you will have the opportunity to right-click on the default signature appearing in the new message. Right-clicking presents a list of all signatures for selection -including the blank signature.
If you would like the message sent without a signature, select "blank" and the mail will be sent without appearing to have a signature line.