Hirsutism is fundamentally an androgen-driven problem, so the trick is to find the agent that lowers androgen action rather than raising it.
Three options push androgens up or mimic them. Danazol is itself a synthetic androgen, so unwanted hair is a predictable side effect. Norethisterone is a 19-nortestosterone progestin that retains androgenic character, again favouring hirsutism and acne. Phenytoin works through a different route but is a classic drug cause of excess hair growth and coarse skin.
Flutamide is the mirror image. It is a pure androgen-receptor antagonist, and clinicians prescribe it to suppress androgen-dependent hair growth. A drug used to treat hirsutism cannot be the one that causes it.
So the exception is the antiandrogen.
\[\boxed{\text{Flutamide}}\]