I've used this technique before and just used acrylics for the "white" wash. I always avoid using pure white for eyes on any figure, and with zombies I definately use an off-white.
The paint shouldn't be a typical wash consistency because it will run into the creases of the eye lids and leave a pale line there. All the paint needs to be is a slightly thinned off-white which will not fully cover the pupil and iris you already painted, giving a nice milky eye
hope some of this rambling helped!