Update theme to PHP7

Hello, I’m trying to run WP on PHP7 but I get an error 500 because my theme uses some PHP4 code. I would like to repair the theme myself.

The problems are here:

class widget_flickr extends WP_Widget { 

	// Widget Settings
	function widget_flickr() {
		$widget_ops = array('description' => __('Display your latest Flickr Photos', CORE_THEME_NAME) );
		$control_ops = array( 'width' => 300, 'height' => 350, 'id_base' => 'flickr' );
		$this->WP_Widget( 'flickr', __('Core Flickr', CORE_THEME_NAME), $widget_ops, $control_ops );
	}

and here:

class TinyMCE_Shortcodes {

	// Constructor

	function TinyMCE_Shortcodes () {

		//admin_init
		add_action( 'admin_init', array( &$this, 'init' ) );

		//Only use wp_ajax if user is logged in
		add_action( 'wp_ajax_check_url_action', array( &$this, 'ajax_action_check_url' ) );

	}

The PHP Compatibility Checker plugin reports for both the following error:

Deprecated PHP4 style constructor are not supported since PHP7

Now, I would easily change the function name with the __construct equivalent, but I’m not sure this would be enough.

Can you help me? Any suggestion is appreciated.