The evidence against Oswald is overwhelming. He left the murder weapon at the scene of the crime. The probability of his conviction is about 99.9%. The kinds of nutty claims that most CTers have relied upon to create false doubt of his guilt are not persuasive given the dubious and often outlandishly laughable nature of such claims. Even after 50 plus years to trying. The tolerance for such kookery in Texas during the 1960s would have been much less than today. Any nut can blame the JFK assassination on UFOs or people hiding in the bushes on the Internet, but imagine what a 1960's era Texas judge would have done with that nonsense.
I agree that Oswald would probably have been convicted, but only if the evidence presented against him was constrained to it being his rifle, and his having no one who could vouch for his whereabouts at the exact moment of the shooting.
If the prosecutor over-played his hand, and brought in stuff like the fibers supposedly found on the rifle, the palm print supposedly found on the rifle, the gsr found on Oswald's hands, and a reluctant eyewitness who later changed his mind, it could have collapsed, IMO.