Nope...don't buy the non-violent end to the Neanders for one reason: the rapidity of their disappearance from the Euro scene. They were there one minute and gone the next. Your gene-swapping theory could work if the timing were MUCH slower... If CroMag had a distinct advantage as a hunter (eg, verbal abilities that made it easier to coordinate a group of hunters bringing down large game -- which is not easy to do if all you've got is spears and thrown rocks), he could strip a Neandethal hunting territory of game in short order. They wouldn't have to come into direct conflict with each other -- one would be able to survive in an area that the other would starve in
Yes...you could be right, but you would have some 'splainin' to do: 1) why would one posit Cro Magnon being non-violent to another hominid hunter in his environment? The whole of human history (from the biblical wars, Asian dynasties, Egypt, Greece, Rome, Vikings, etc., etc., etc.) is one of warfare, violence and elimination of enemies. Why should we ever think it different 35K years ago? With human histroy the way it is there needs to be a bit of a precedent for believing your hypothesis.
And 2) IMHO their disappearance was too swift even for your scenario.