Deadly strike does work for WW, but deadly strike and critical strike roll separately.
In your case, you have 55% chance to DS + (100%-55%)*30% to CS, which would result in a total of 68.5% to do double damage instead of the 85% you were thinking of. --- In memory of one of my favorite manga artists, Usui Yoshihito. May your soul rest in peace. Sep 20, 2009.