Moor

Вопрос решен.
Добавляем еще одно меню в functions.php, после чего в header.php:

if(is_page( pageID )) {
    if (has_nav_menu('primary')) {
        wp_nav_menu( array('theme_location' => 'primary','container' => false,'menu_class' => 'nav uppercase font-primary','walker' => new Vntd_Custom_Menu_Class())); 
    } else {
        echo '<span class="vntd-no-nav">No custom menu created!</span>';
    }
} else {
    if (has_nav_menu('SECONDARY_MENU_NAME')) {
        wp_nav_menu( array('theme_location' => 'SECONDARY_MENU_NAME','container' => false,'menu_class' => 'nav uppercase font-secondary','walker' => new Vntd_Custom_Menu_Class())); 
    }
}