You couldn't even make it into a movie script because it would be so unbelievable.
A 52 year old man that has no history of crime and who most considers somewhat "feminine" sees Palme and decides to shoot him on a whim. With a revolver he carries in his purse this night. Then he flees the scene but returns ten to fifteen minutes later. None of the other dozen witnesses who are still there and are being questioned by the police recognizes him and he blends in as just another witness. Then instead of keeping a low profile he contacts the police the following days and offer to testify. He also does several interviews in the media over the years. Fourteen years later he dies in an apparent suicide never having told anyone about the murder.