If all you need is to prevent Unity from delivering a prompt with the external number, or the internal subscriber information, you just need to remove a check box in the subscriber's conversation config.
Subscriber > Conversation > Before playing each message, play
Sender's information
Message number
Time the message was sent
Uncheck the "Sender's information". This will keep any caller information from being delivered to anyone retrieving the messages from this subscriber's voicemail.