[Steven Zahm]

@ chris429

oh, oh, oh … wait… The exclude_category and show_empty_categories will have no effect when only the category drop down and search are displayed because those are template options. This code snippet basically hijacks the process to display just the category drop down and search box until a search is performed, then the actual template is used. After you do a search the Uncategorized category is not present, correct?

Not sure if this will work … but try adding this to the shortcode:
exclude='1' show_empty='0'