Where are all your phones registered? Assuming also with the sub, then you should be fine. However, I would only do this during a maintenance window.
I would double check that both JTAPI providers/CTI managers are properly programed and running. And if using DC Directory that it is running on the subscriber and that it is programmed in the LDAP information. Then reboot after hours.
On the CRS server goto System > LDAP Information > LDAP Server hostname... There you can enter the primary and secondary LDAP server hostnames/IP addresses. If you only have the publisher entered there, then when you reboot you could have issues with agents logging in, etc... If that's not a problem, go ahead and reboot. Also this information is only for DC Directory, if you are using an external LDAP (MS AD or other) then you can disregard. You can also take a look at the "Help for this page" in the help menu.
That would make sense during restarts of the publisher we have issues. Just checked the settings and we only have our pub, so I can add both of my subs as long as I have DC Directory running on those servers? After make this change is a reboot required?
You should have only 2 CTI Manager enabled, since it seems you have 2 subs and one pub it should be disabled on the Pub and started on both sub configured as Primary and Secondary in the IPCCX LDAP info.