Responsibility is the wrong word here. If women want certain behaviors to stop, it is logical for them to explain exactly what they don't like. Expecting already awkward men to read minds is self-defeating.
It is not logical for a woman (or anyone really) to remain in a situation that makes her uncomfortable and especially not logical to remain in a situation where she fears for her safety. Responsibility was the correct word--the onus on creepers to stop being creepers, not the women who are being creeped on or harassed to explain why that behavior is inappropriate.
Of course there are many situations where simply removing yourself isn't the end of the story--coworkers, friends of friends, etc. One should be encouraged to speak up in situations where they are made to feel uncomfortable, especially considering that "creepy" itself is a subjective experience. But its not that they have a responsibility to, it's simply an effective way to communicate your wishes to another person. Expecting someone who is being creepy to just know that they're being creepy seems almost oxymoronic.
Women/people certainly CAN choose to educate. Your presumption that she SHOULD or, rather, "The proper way to handle this issue is..." is what I took issue with. There is no "proper way to handle this issue" except the way that makes the violated feel safer. If that means she moves away from the perpetrator, then that is proper way. If it means opening a dialogue about improper behavior, then that is the proper way too. Ultimately, it comes down to the woman/person in question.
Also, awkward isn't synonymous with creepy. See rosser's reply elsewhere in this thread for a better explanation of creepy: https://news.ycombinator.com/item?id=5975094