You have to create a db with all databases and they passwords and servers (to connect to the other servers) and retrieve the version, or create a plugin to wordpress that prints the version only if you send some password from get or post (for security reasons), and install it into all wordpress systems, then you only have to read the plugin url. (this is usefull if you don't have direct access to the mysql, this happens on some hosting companys that have the mysql db on a closed network. )
If i were you, i would opt to choose my secound option (bolded)
EDIT:
Please in the plugin use Hash protection, or something like that:
Your Platform Side:
<?php
$mypass="test123";
$version = file_get_contents("http://www.example.com/yourpluginurl?pass=".md5($mypass+date("d")));
if(isset($version) && $version !== false){
//your code here
}
Plugin Side:
<?php
$mypass="test123";
if(md5($mypass.date("d")) == $_GET['pass']){
//Get version here
}
?>