The DHCP clients will only register in the zone if configured to do so. You can turn that off.
If you have a local DNS and DHCP server in each location then only syncing those zones will go across the WAN. However, even with multiple zone, if they are ActiveDirectory integrated, they will still sync across the WAN, so no gain there. You can tune how often the sync takes place though.
The zone is created for a domain though, so you would have to create a whole new domain. You might be better off using sub-domains for this - uk.domain.com, us.domain.com. But, as I said above, if using ADI the data will still sync.
However, with local servers, the local PCs will see less latency when they request an IP and it gets added to DNS. That addition to DNS won't impact the client at all though, as it is distinct from the IP granting process.
Are you actually seeing an issue here or just generally looking to improve performance?