Response to "Would you not do it?"

I would use the first one as "No" asserts negativity. The following Wikipedia post could be helpful here:

According to Grimes, the answer "yes" asserts a positive answer and the answer "no" asserts a negative answer, irrespective of the form of the question. But in fact simple "Yes" or "No" word sentence answers to yes-no questions can be ambiguous in English. For example, a "Yes" response to the question "You don't beat your wife?" could mean either "Yes, I don't beat my wife." or "Yes, I do beat my wife." depending from whether the respondent is replying with the truth-value of the situation, or is replying to the polarity used in the question. This ambiguity does not exist in languages that employ echo answers. In the Welsh language, for example, the response "ydw" ("I am") has no such ambiguity when replying to a question.