Looking at the source to Authen::NTLM, there is nothing in there that will grab the username and password for the currently logged in user. In fact, I'd venture to say that it's not possible to obtain the cleartext password for the current user. All the ntlm_password() sub does is to return a password you set earlier by using, for example, the new contructor for Authen::NTLM.
Unfortunately, if you don't have a way of actually obtaining the username and password (e.g. from a configuration file) to use in this script, I don't think this approach is going to work for you. And, while I'm no expert with Win32 in Perl, I don't know of any approach that will, short of installing Outlook.