Best way to change Server IP

[Imai]

I am planning to change networks meaning I will get a new block of IPs.
I can change the server IP from WHM but my concern is some of the domains have dedicated IPs with SSL.

Does anyone know how change the IPs for these domains without problems.

I will appreciate it if someone points me to the right direction.

Thank You

[Imai]

Sorry I should have made my question simpler.

I want to know if the process of changing server and site IPs will be effected smoothly.

I am using class C addresses for illustration.
Say my main server IP is 192.168.100.100 and I have a site with dedicated IP 192.168.100.120. This site has ssl certificate installed on this IP.

If I change the server IP to 172.10.100.5 and change the site's IP to 172.10.100.24.

My questions
1. Will these changes take effect without problems?
2. Do I need to do anything special about the ssl certificate?
3. Has anyone gone through this process before

I will very much appreciate a response.
The site is in production and the client can't afford downtime
but we have to move our network.

Thank you