Override header.php with one in plugin's folder

Hi there,

I’m creating a plugin that make use of a custom post type, i need it to be theme-independent so i am overriding the template with my own which is in my plugin’s folder, this is how i do it:

define( 'PLUGIN_PATH', plugin_dir_path( __FILE__ ) );

//Template fallback
add_filter( "template_include", 'ps_theme_redirect' );

function ps_theme_redirect( $template ) {
    //cpt is the slug of the custom post type registered
    if ( get_post_type() == 'cpt' ) {
        if ( is_single() ) {
            //looks in the current theme directory for the template if so it is returned otherwise the template from the plugin directory is returned.
            if ( file_exists( get_stylesheet_directory() . '/single-cpt.php' ) )
                return get_stylesheet_directory() . '/single-cpt.php';
            return PLUGIN_PATH . '/templates/single-cpt.php';
        } else {
            if ( file_exists( get_stylesheet_directory() . '/archive-cpt.php' ) )
                return get_stylesheet_directory() . '/archive-cpt.php';
            return PLUGIN_PATH . '/templates/archive-cpt.php';
        }
    }
    return $template;
}

Now i need also to do this with the header because i don’t want to show menus and stuff that a theme might have in header.

Can anyone please advice on how to do this? Basically i need to override theme’s header.php with the one i have in my plugins folder.

Thanks in advance,
Stelios