IP addresses don't matter at all (except for the rare case where people have used an IP address in the display URL.)
I'm a bit confused, though, by your use of the term "redirect", and by this statement: " this would be a redirect of my old IP address to the new IP address by the host". Huh? Why not just change the DNS A record(s) for the web site? You just need to change where the domain points to. No need for any kind of redirect.