Andropause is what happens when T levels drop, menopause is when E levels drop.
Personally I would say dropping T levels first is a good idea, because estrogen can amplify the andropause symptoms dramatically, the andropause symptoms are also most active when testosterone is on the decline, and dropping T levels really fast is not a good idea, because that will cause you to have more symptoms, so slower is better, but once T levels have been dropped for so long the symptoms will drop to, my doctor told me he would have done it this way if I had got to him before self medicating, always get a doctors advice before taking anything.
Anti androgens some times, for some people, cause something called Gynecomastia (male breast growth) some get full on feminine boobs, while others will end up with man boobs, but it depends on the person, but this doesn't happen to everyone that uses an anti androgen for monotherapy.
If you do decide to do this, be shore to have some estrogen near by, so if boobs begin to develop you can avoid the possibility of the dreaded man boobs.