If any of you nerds have honestly tried a reconstruction you will find that the package is too heavy to carry strictly in the palm. It forces one to curve the wrist under the bag as Rather is seen doing here. Not an efficient carry method.
To say that Buell never saw Oswald use the left hand simply confirms that he did not possess Xray vision, since Buell was behind Oswald as the little prick hot-footed away to make sure his chauffeur didn't get a full-profile look at the gunbag.