Okay, so, as mentioned in my comment to you: altering core files is not a good idea.  But here is a plugin solution.

First we're going to create our own rewrite rules that rewrite `s/123` (replace 123 with a post ID) to `index.php?short=123`.  We'll also have to filter the WordPress query variables so we can use them later.

    <?php
    add_action( 'init', 'wpse26869_add_rewrites' );
    function wpse26869_add_rewrites()
    {
    	add_rewrite_rule( '^s/(\d+)$', 'index.php?short=$matches[1]', 'top' );
    }
    
    add_filter( 'query_vars', 'wpse26869_query_vars', 10, 1 );
    function wpse26869_query_vars( $vars )
    {
    	$vars[] = 'short';
    	return $vars;
    }

The `add_rewrite_rule` call says "rewite s followed by a slash and a string of one or more digits to `index.php?short=the_string_of_digits`.

Then we can hook into template redirect and see if our query variable is there. If it is, we'll try and get a permalink out of it.  If that fails, we'll throw a 404 error.  Otherwise, we'll use `wp_redirect' to send folks to the actual post.

    <?php
    add_action( 'template_redirect', 'wpse26869_shortlink_redirect' );
    function wpse26869_shortlink_redirect()
    {
    	// bail if this isn't a short link
    	if( ! get_query_var( 'short' ) ) return;
    	global $wp_query;
    	
    	$id = absint( get_query_var( 'short' ) );
    	if( ! $id )
    	{
    		$wp_query->is_404 = true;
    		return;
    	}
    	
    	$link = get_permalink( $id );
    	if( ! $link )
    	{
    		$wp_query->is_404 = true;
    		return;
    	}
    	
    	wp_redirect( esc_url( $link ), 301 );
    	exit();
    }

Finally, we hook into `get_shortlink` to change how our rel="shortlink" appears in the `<head>` section of the site, and elsewhere.  This new shortlink structure will reflect the rewrite rule we wrote above.

    <?php
    add_filter( 'get_shortlink', 'wpse26869_get_shortlink', 10, 3 );
    function wpse26869_get_shortlink( $link, $id, $context )
    {
    	if( 'query' == $context && is_single() )
    	{
    		$id = get_queried_object_id();
    	}
    	return home_url( 's/' . $id );
    }

As a plugin:
https://gist.github.com/1179555