Run a filter when a walker runs

If all of it is your own code then it would be reasonable to just implement that as part of walker.

If you need to add a filter while third party walker runs you could probably:

Add it at wp_nav_menu_args hook, checking if walker is set to that:

add_filter( 'wp_nav_menu_args', function( $args ) {

    if ( $args['walker'] instanceof megaMenuWalker ) {

        add_filter( 'wp_nav_menu_objects', 'callback_name_here' );
    }

    return $args;
} );

Remove it at wp_nav_menu hook after the menu markup is completely generated:

add_filter( 'wp_nav_menu', function( $nav_menu ) {

    remove_filter( 'wp_nav_menu_objects', 'callback_name_here' );

    return $nav_menu;
} );