Dallas Police Sergeant Gerald Hill radioed from the scene of the Tippit shooting to the Police Dispatcher and said: “The shells at the scene indicate that the suspect is armed with a .38 automatic or semi-automatic handgun rather than a pistol.” (pistol - a/k/a a revolver or wheel gun).
Oswald was captured with a .38 Special Revolver.
There is a substantial difference between an automatic and semi-automatic handguns, which ejects discharged shells immediately, automatically, versus a revolver, which requires deliberate opening of the weapon to empty the discharged shells.
Automatic and semi-automatic handguns also require different types of ammunition, which cannot be used and fired interchangeably from a gun not designed for its specific use, anymore than you can fire different caliber ammunitions in a gun not specifically designed for its use.
Finally, it is beyond comprehension that any trained shooter who just killed a Police Officer in broad daylight would stop to open and empty his discharged shells from a revolver, and further risk being seen, identified, chased, and/or captured.
The only realistic analysis of this scenario that could possibly make sense would be to plant evidence.