hardek: What brand is marked on the box? If Winchester, chances are your ammo is the modern, solid base type. When Winchester introduced the Model 1894 rifle...which was well into the smokeless powder era, one of the chamberings was .32-40. Many cartridges of the time were being produced with the new, solid base design. The .32-40, among them. Though it's known that early, .32-40 ammo was loaded with black powder. Several sources mention that Winchester produced black powder .32-40 ammo, up to around 1940. So, this may be what you have.
Only way to know for sure, is to cut one in half, lengthwise. Then, it should be easy to see which type it is. If the older, balloon-head type, don't load them. They are often too weak to handle smokeless powder operating pressures.
By the way, if you can't find any new .32-40 ammo or brass for reloading, 32-40 brass is relatively easy to make. Either resize .38-55 brass. Or: .30-30. Easiest to form from .38-55 (long) brass. Rusty Wood shows Starline brass, in stock.