I agree, Edward of Westminister's birth is not responsible for the Wars of the Roses, nor is there any serious doubt about his paternity. Henry VI was very pious -- the reason he was married for several years before his son was born, and there were slanderous rumors about Edward's paternity, but still, Henry VI was his father.
If you are looking for a way to prevent the Wars of the Roses, I'd say the best thing is to prevent Henry VI's insanity or general terribleness as a king. Henry VI simply did not possess the capabilities to rule England during such a turbulent period, and that is the reason for the start of the Wars of the Roses. Edward of York would have never rebelled had he not been excluded from exercising legitimate power and the court party had not dominated affairs to such a degree.
Also, having a less kick-ass and strong willed wife might have prevent the Wars, because she was the one that dominated Henry VI and prevented him from being dominated by others, such as Edward of York of the Duke of Somerset.
Scipio