How do I set an empty search domain on Airport/Time Capsule
On the AirPort or TimeCapsule that is acting as DHCP and/or NAT, placing a period “.” in the Domain Name field will push a null domain name search to its DHCP clients…  

It does this by making yer DHCP clients’ treat hostnames as fully qualified…  That will not disable domain name searches on the DHCP clients if they are configured to use search domains…  

BUT, it will eliminate having yer ISP’s domain name appended as an additional domain name search…  With the added benefit of slightly faster DNS resolutions eliminating parent and child domain searches…