PAA – I can not speak for R’ Chaim being that I have not asked him directly. It is obvious, however, that he is in great opposition to WOW.
I would venture to say that according to everybody, including the Ben Ish Chai who holds that there is a problem of Beged Ish, the main problem here is that these WOW women are Mizalzel B’Torah U’Mitzvos. The fact that they as a whole are not Shomrei Torah U’Mitzvos shows that their wearing Tefillin has nothing to do with dedicating themselves to Torah, but rather they are feminists that found their niche in feminism; namely “defend” women from chauvinism in Judaism. Unfortunately, in order for a cause to take off you need backers and they are clearly not getting support from their religious counterparts.