First of all, surely even the most vitriolic man-hater must realize that if all men on Earth die, the human race would go extinct within decades (Yes, I know about Valerie Solanis and her views, but she was a psychopath). The way I imagine a feminazi dystopia would be where men and boys are kept as slaves, and once they mreach a certain age, say 18, they are sent to die in wars between warring "womyn" factions over Earth's dwindling resources.
Second, a virus would take a few weeks or months to spread around the world, and once Russia and China catch wind of the scheme, they'd demand the vaccine for themselves and threaten to launch their nukes if they don't get it. Than the whole human race would be fucked, not just the men.