The generate_header hook is inside your header.php and is where your entire header element is hooked into.
It sits between the generate_before_header and generate_after_header hook.
You can use this hook to completely remove the
add_action( 'after_setup_theme','tu_remove_header' );
function tu_remove_header() {
remove_action( 'generate_header','generate_construct_header' );
}
Learn how to add PHP here.