It depends on the NAT.
If you are using static NAT statements from the same IP subnet as your outside interface IP then for ASA firewalls at least they use proxy arp to respond to arp requests from the ISP router.
If the Watchguard works on the same principle (and I don't know whether it does or not) then you cannot have them both responsible for the same IP as they will both respond to the arp and it is a lottery as to which one wins.
The additional problem with the above is the ISP router will have an arp entry in it's cache for that IP. If you move it to the new ASA then you would either -
1) have to tell the ISP to clear that entry from their router's arp cache
or
2) wait until it times out before it will work.
All of the above applies to IPs from the same IP subnet as the outside interface IP but not the outside interface IP because that will be probably be used for dynamic PAT for users accessing the internet so the ISPs arp cache is constantly updating.
If the IPs are from a different network altogether and none of the IPs are assigned to any interfaces on the firewall then presumably the ISP will have a route for that subnet pointing to the outside IP of the existing firewall so this may need updating but then you would to need to move the whole subnet at once really.
The final possibility is if the IPs are from a different network ie. not assigned to any interfaces but the ISP relies on proxy arp again to resolve them.
Same issues with arp cache as before and with the ASA you may also need to allow proxy arp for non connected networks.
Difficult to be precise without knowing exactly what you are using.
Jon
