I need a custom search page to lead to search.php but it goes to index.php

If I get it correctly WordPress loads the search template dynamically by the parameters delivered to it. Specifically the s parameter. Meaning if you try to send the user to the http://www.example.com/search.php you’ll get 404 error page.
For now the only workaround I can think is to create a function which is hooked to the init action hook that listens for a parameter in order to load the right file. The function must reside in the functions.php of your theme (assuming you are developing a theme). The function goes like this:

function load_custom_search_template(){
    if(isset($_REQUEST['custom_search'])){
        require('my_search.php');
        die();
    }
}
add_action('init','load_custom_search_template');