You want to use the an SPListItem's CreatedBy or ModifiedBy values and the OpenXml API to do this so you do not have to use the Word Object Model on the WSS/MOSS Server.
To obtain the user information, you'll want to to something like this.
//get the SPWeb reference for web
SPFile updatedFile= web.GetFile(fileUrl);
SPUser author = updatedFile.Author; //or updatedFile.ModifiedBy for modifier
Once you have the author, to update the Word document, you can refer to this SharePoint and OpenXml wiki page for some assistance. This is based on Eric White's blog (and others) with Open Xml. I highly suggest you read his blog and look at the PowerTools for OpenXml Codeplex project for some code that will definitely be helpful.
Also see OpenXmlDeveloper and Open XML Developer portal for more information
Hope this helps.