Few people know this, but NIP-17 DMs are all yours to control. It doesn't matter if you sent them or if you received them. 

Your DM relay can delete them at any time YOU want them to without affecting the other party. 

You can download all your messages, both sent by you to your friends and sent by your friends to you, delete everything and even re-wrap and republish them all back to you. The sender cannot stop you. And you don't need the keys of the sender to do any of this.

If you want disappearing messages but your peer wants to keep them, you both can be served. Because once a DM event is received, it is completely detached from the sender or any other external state that must stay in sync with yours.

All the power to you.