The first answer from jornane is correct so far as it goes, however I do not believe it addresses what the OP is really trying to get at - which is how best to handle migration of email and accounts, rather than how to handle DNS.
Ordinarily there are many ways to handle this task, but because we are dealing with only one server which will be going through an OS reinstall. I will take for granted OP's assertion that yum has somehow become irreparable, or so damaged that repair would be more complex or time-consuming than reinstalling OS. I will also take for granted that this is your only available server, and that you are familiar with imapsync. I am also going to assume that you are using dovecot-imapd as your IMAP server, because postfix is an SMTP server and not an IMAP server (but dovecot I find is one of the more widely used IMAP systems with postfix).
One option in this scenario is to use imapsync to backup your accounts to a series of free gmail accounts. Backup each account to gmail (you could do several simultaneously, depending on how much muscle your current server has and what kind of anti-spam tactics Google is using for IMAP lately). You can use this script:
imapsync \
--host1 your.oldserver.ext --port1 993 --user1 [email protected] \
--passfile1 /path/to/gmail_mirror.passfile1 --ssl1 \
--host2 imap.gmail.com --port2 993 --user2 [email protected] \
--passfile2 /path/to/gmail_mirror.passfile2 --ssl2 \
--useheader 'Message-Id' --skipsize \
--syncinternaldates --noauthmd5 -nofoldersizes \
--split1 100 --split2 100 \
Note that this relies on the default IMAPS TCP port 993. If you are using plaintext IMAP on your server, you should consider not doing that as soon as possible, and in the time being you can change your port to 143 or whatever you are using. You can probably also use localhost for host1 in the first script and host2 in the second script, again depending on your settings. You will also need to use a passfile. More info on the correct flags to use and how to use them is available here: http://imapsync.lamiral.info/OPTIONS
To dump the emails from Google to the new server you can do this, which will work for your All Mail and Sent Mail folders:
imapsync \
--host1 imap.gmail.com --port1 993 --user1 [email protected]
--passfile1 /path/to/gmail_mirror.passfile1 --ssl1 \
--host2 your.newserver.ext --port2 993 --user2 [email protected]
--passfile2 /path/to/gmail_mirror.passfile2 --ssl2 \
--useheader 'Message-Id' --skipsize --allowsizemismatch \
--syncinternaldates --noauthmd5 -nofoldersizes\
--split1 100 --split2 100 \
--regextrans2 's/\[Gmail\]/username\@somedomain/' \
--include "All Mail|Sent Mail" --delete2 --expunge2
The advantages to this approach is that the likelihood of it breaking something is very small. Because I am working from the assumption that yum is irreparably damaged, and because I am unfamiliar with this server, it is very possible that other components are also broken or corrupted. This method is very simple and leaves little room for subtle failures.
There are other options that have additional benefits: most notably, other backup and restore options would be much faster as they would not depend on internet connections. However, exploring those options would require more detailed information about your environment, for example: does your server in fact use Dovecot to provide IMAP or another program? Does your server use some CMS like cpanel or Plesk? Does your IMAP daemon have a MySQL backend? Do you use system or virtual users?
Keep in mind that there are a variety of ways that a mail server migration can be complicated. There are a variety of different authentication schemes for example that could complicate the migration of users and their mailboxes as opposed to simply transferring their email as I have laid out here. If you want to recreate users that can send using SMTP using the same architecture as your prior server, we would need to get a look at the relevant portions of your main.cf and IMAP configuration files (for dovecot those would be dovecot.conf).
