What greater thrill (for anyone but a fiendish cleaner) than to watch someone with no personal interest in your apartment willingly attack such unfamiliar terrain as the tops of door frames, the undersides of sinks, and the flooring beneath radiators? "This is a true spring cleaning,'' assures Joab Hamilton, of White Glove Elite (1265 Broadway, near 31st Street; 684-4460). Hamilton actually sings as he vacuums; he picks up knickknacks, cleans underneath, then replaces them in better order. The agency can generally send someone with 24 hours' notice -- even on a Sunday. While White Glove is $17 per hour, with a four-hour minimum, good services are available for slightly less money. The cleaners from Maids Etc. (500 Park Avenue, at 59th Street; 223-4455) are speedy, kind, and caring and cost $12.50 an hour (four-hour minimum).