Some times you just have to laugh at yourself ... I was just struggling to figure out how to hide the Body field on a new CCK form, and just as I was thinking I might have to resort to some jQuery magic, I finally read the help text under the Body field on the CCK "Submission Form Settings":
To omit the body field for this content type, remove any text and leave this field blank.
How funny. Sure enough, I removed the simple "Body" label I had typed in there without thinking earlier today, and my CCK Body field magically went away on my new CCK content type.
If you can't find it, with Drupal 6 you should be able to find the Body Field Label field and corresponding help text at a URL for your website that looks something like this:
http://yourwebsite.com/admin/content/node-type/your-content-type
So, if you're trying to get rid of a Body field on a new Drupal CCK content type, I hope this short blog post is helpful to you.