I'll toss a couple of ideas out to you...
First, the service "network" on RH boxes is a better choice to refresh your networking. However, it is file driven for its configuration. Which brings me to my next point.
If you ONLY make the changes through ifconfig, these are RAM-only changes that will be lost when you next reboot the box or restart the network service. At such point, you will revert to the settings in your config files...
Sooooooooooooooooooooooooooooo...
Spend some time thinking about the contents of these two files:
/etc/sysconfig/network
/etc/sysconfig/network-scripts/ifcfg-eth0
Between these two files you will need to make the relevant changes to your IP, mask, broadcast, gateway, and network settings (a couple of which you might not have thought of in your first scenario)
You can make changes to these files and they won't impact the system until you either reboot or issue
"service network restart"
You WILL (99%) lose your connection to the server upon either method of restarting...
ALSO!!!! Make VERY sure that you understand your firewall rules. RH has a habit of there being some default firewall rules that are ENABLED when you build the machine. Generally these rules are written agnostically to your IP addressing scheme, but I recommend you be sure by checking iptables before you restart.
Beyond these points you would minimally want to ensure that any IP-specific assignments in your major service configuration files are managed before rebooting.
Generally 'sshd' is NOT bound to listen on a specific IP/mask, so unless you did it specifically you probably are ok.
Often 'httpd'/apache is bound to listen on a specific PORT not IP, but depending upon your environment, it might have been configured for specific IPs.
You may want to let this thread run for a day to see if anyone else spots ways to control your risks before you make your changes.... good luck!
D.E.R. Management - IT Project Management Consulting