wp_nav_menu container style args

See if I correctly understand your meaning.
For argument details, you may wish to refer to wp_nav_menu()

When you call the menu, you may add the following arguments:

wp_nav_menu(array(
        'theme_location' => 'primary',
        'container'      => 'div', // default is div anyway, you set it false because you want to add ID, right?
        'container_id'   => 'container_id', // container id here, css ID for container above

        // comment out if you need
        // 'menu_class'  => 'menu-class-here', // menu class
        // 'menu_id'     => 'menu-id-here',
        'fallback_cb'    => false,
        'depth'          => 5
));