wp_nav_menu() (in includes/nav-menu-template.php) applies these filters after a menu has been ‘walked’ (ie. filtered by CMW and built as HTML list items)…
// Allow plugins to hook into the menu to add their own <li>'s
$items = apply_filters( 'wp_nav_menu_items', $items, $args );
$items = apply_filters( "wp_nav_menu_{$menu->slug}_items", $items, $args );
and after wrapping in a container (if applicable)…
$nav_menu = apply_filters( 'wp_nav_menu', $nav_menu, $args );
You can test for the CMW widget (specifically) having processed the menu by checking…
if( !empty( $args->_custom_menu_wizard ) ){ .... }
Is that the sort of information you need?
