load-{$page hook} and returned parameter

//is there a $param here?

None, the hook you’re using does not pass any parameters to the callback.

But you can instead use the admin_enqueue_scripts hook which passes the hook name for the current menu page — the hook name is also saved in the global $hook_suffix variable. You can then use get_plugin_page_hookname() to get the hook name for a specific menu page and then conditionally enqueue the scripts for your menu pages.

function my_admin_enqueue_scripts( $hook_suffix ) {
    switch ( $hook_suffix ) {
        // Enqueue scripts for the "Audio Player -> Settings" page.
        case get_plugin_page_hookname( 'my_settings', '' ) :
            //wp_enqueue_script( ... );
        break;

        // Enqueue scripts for the "Audio Player -> Player manager" page.
        case get_plugin_page_hookname( 'my_player_manager', 'my_settings' ) :
            //wp_enqueue_script( ... );
        break;
    }
}
add_action( 'admin_enqueue_scripts', 'my_admin_enqueue_scripts' );

And actually, you should use the admin_enqueue_scripts hook for enqueueing admin scripts. 🙂

Additionally, in your first add_submenu_page() call, you should just omit the sixth parameter (i.e. the callback) than setting it to my_settings_page, to prevent the function from being called twice on the same page.