Remove “minor-publishing” div from Publish admin metabox

In short- no. The html in question is hard-coded in the post_submit_meta_box callback function.

You can, of course de-register the publish metabox and re-register your own which mimics post_submit_meta_box (but making your alterations) and being sure to keep the names of the inputs exactly the same. This method has been outlined the following posts where a core metabox is required to be edited.:

• custom post type taxonomies UI radiobuttons not checkboxes
• Custom-Taxonomy as categories: Remove “most-used” tab?

It’s a lengthy function though – and would break if core ever changed decided to change the names of the inputs (though very unlikely).

In this situation I would probably recommend a CSS or javascript work-around….