I did a google search for 'no kill shelters washington state' and ran across this site:
http://fluffynet.com/no-kill-shelter...kill-shelters/
You could also search for no kill shelters near the city where he lives.
Beyond no kill shelters, you can also look for general rescues/cat rescues in the area.
If they happen to be a special breed of cat (siamese or siamese mix or other breed), you can also look for rescues specific to the breed.