My best advice? Get rid of the POP account. To be honest, I'm not sure exactly what would happen when you restore your backup with the POP account. Looking at this comparison of backup data, About backups for iPhone, iPad, and iPod touch - Apple Support I'm not sure exactly what kind of mail data is backed up. It isn't real clear. I'm not exactly clear what will repopulate when you log back into the phone. I cannot guarantee that the content of your POP account will be there, but I can say that if it is, when you log back into the server, since there won't be any mail on the server, it won't do anything to the mail you currently have. That is how POP works. It downloads the mail to the client and leaves it alone to be managed on the client. I'm just not sure how it may repopulate your folder arrangements.
As far as sending the mail back to yourself, I guess that would be an option, and when you log back into the account, if it is on the server, it will get downloaded again. If you leave the content on the old phone and restore your phone to your current backup of the old phone, you will see what you have before you wipe the old phone and you can decide from there. You can also take a look at the information here for using Quick Start and see if that transfers all of the mail info to the new device as well. Use Quick Start to transfer data to a new iPhone, iPad, or iPod touch - Apple Support
