Welcome to the Forum. Your S&W is a .32 Double action and 162843 would be a 4th model probably made around 1896, or so. It is an antique under Federal regulations as it was made before Jan. 1, 1899. The correct ammo. is the .32S&W cartridge. The round you have that is too long is a .32S&W Long cartridge, made for later models. The gun looks to be in very good condition and if mechanically tight, should fire the .32S&W rounds safely, however the parts are delicate and replacement are hard to find. 1,000s of these were made, so values are not high unless the guns are near new in their original boxes. My condolences for the loss of your father. Ed.