Well it really depends. Do you have full control over this server, or simply a shared account on it? If you don't have full control then you can't 100% use a dedicated IP.
Depending also on the control panel installed depends on what can be used to route the mail. For instance cPanel with exim has the option to select the mail IP for each domain name for outbound settings, after that's set then simply update the forward and reverse dns to match.