I would suggest that Shakespeare does not so much use androgyny as, rather, allude to male and female traits—in the way they are conventionally understood—as a means of explaining or clarifying the motives and actions of his characters.
Lady Macbeth's famous wish to be "unsexed" indicates that she herself believes that, as a woman, she doesn't have the qualities required to plot or carry out a murder. Other things about her behavior suggests a stereotyped femininity. She urges Macbeth to commit the murder of Duncan rather than doing it herself. This is a case of her using her "feminine wiles." But one could interpret the wish to see her man become successful as a positive trait (though in this case severely misguided!) motivating her rather than pure selfishness.
However, in more than one scene, she tries to humiliate Macbeth by questioning his strength and his masculinity. When the ghost of Banquo appears and Macbeth becomes hysterical, she pointedly asks him, "Are you a man?" and then:
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