You are quite right. 'I want not to do something' is a strange thing to say in most situations. The opposite of 'I want to do this' is - obviously - 'I don't want to do this'. If you want to express a lack of desire to do something, you put the verb 'want' into the negative, not the verb 'do'. I think that you are over-applying some grammar which is intended for a different use. 'Not to do' is a negative infinitive. For example: He agreed to do this. He agreed not to do this.