I would like to try a new cookie recipe. See Sebastopol Applesauce Cookies at www.biteclubeats.com. The recipe calls for 2 cups of whole wheat flour. Can I substitute 2 cups white whole wheat flour instead?

You probably could, but it won't taste the same. Most recipes where you want to exchange whole wheat flour for white flour (or the other way around) do well with replacing from 1/4 to 1/2 of the flour with the other kind. So in this case, use one cup of wheat flour and one cup of white flour and it should be okay.