Greetings Eric,
If you’d like to create an output style that produces no formatted bibliography, on EndNote’s Edit Style window, click “Templates” within the Bibliography section and delete each template defined on this window. After removing all bibliography templates, you can either click File>Save to update your existing style with these changes, or click File>Save As… to save a newly-named version of your custom output style.
Please let me know if this works for you.