Of note, you can change the outgoing gateway IP used by email without changing the main server IP. If you select "Reference /etc/mailips for outgoing SMTP connections" in WHM > Exim Configuration Editor and "Save" the area, then add the following into /etc/mailips:
Replace
newIP# with the new IP address. At that point, email sent from the server will use the new IP for routing emails in place of the main IP. As such, if the only reason you are changing the main IP has to do with exim routing, I would suggest doing the above rather than changing the main IP.