If WP widget is active :

is-active-widget.php

<?php
/*
 * @link http://codex.wordpress.org/Function_Reference/is_active_widget
 * In my class (the class that extends WP_Widget)
 */
class My_Widget extends WP_Widget(){

  public function __construct(){
  
    /* some code blabla 
    *****/

    add_action( 'wp_enqueue_scripts', array($this, 'my_callback') );
  }

    /* some code blabla 
    *****/
  
  // enqueue styles for widget but only if it's there !
  function my_callback(){
    if( is_active_widget( false, false, $this->id_base, true ) ) {
        wp_enqueue_style( 'handle', 'path/to/widget-styles.css' );
    }
  }
}

Merci pour cette astuce ;)