If the client is that worried about privacy, tell them they need to manage their own mail. You can not administer a system properly without access to it, this access comes with trust, they either trust you to not mess with their data or they dont.
The *only* way they are going to get a mail system that only they have access to is if they run it on their own. It's also worth pointing out to them that SMTP is a CLEAR TEXT protocol, *ANYONE* in the path of the message can pick it off the wire.
look into end to end cryptography solutions such as PGPMail to encrypt each message before it is sent.
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