You can make your emails available offline by setting up your mail account as pop account, but I do not recommend doing that because I can't predict consequences. If you really want to try - do that one one device and use it for a while until you are confident it works for you.
All you need to do is add a mail account and mistype your password on purpose, on one of the next screens you will be prompted to chose pop or imap.
All you do choose pop and save. It will place all of your email locally, but there is absolutely no guarantee that your changes after you done will be uploaded or any other behavior of IMAP will transfer to POP. I do not know any other way to make all of your emails available for editing offline.
My recommendation would be to leave everything the same and do your work in other text document. When you get back online just copy and paste your replies.