In clusters, leaglebu, balls of approximately that size were grouped and contained in a cluster. Cannister would have been a bit smaller, and grape would have been larger. I'll not insult you with specifics as you may well be aware of them and asking about something else. And I'm not exactly comfortable with the "size of unhulled walnuts." Are we talking run-of-the-mill walnuts? Jumbo premiums? Commercially acceptable?
Basically, grape and cannister had specific sizes and quantities per round per caliber-- which is not to say there were never variants. If you want, I'd be more than happy to entertain more specifics and supply you with such information as is available readily available to me. Which means I'll skim through a couplathree books and then try to accomplish something. Finding an answer would count.
Just occurred to me: we are talking CW field artillery aren't we? Not deck-mounted swivel guns or some such?
Although I am a Civil War researcher, I am ignorant when it comes to the armaments of that war. I asked the rangers at Wilson's Creek National Battlefield near where I live in Springfield, MO and they thought maybe it came from ammo used in siege guns placed in several forts during the Civil War at Springfield, MO.
The size is just a little larger than a standard golf-ball and was found near where the Old Wire Road ran through Springfield. That road ran from St. Louis through Springfield, Wilson's Creek and on down to Pea Ridge, Arkansas.
I saw a History Channel program about how hot air balloons were used by the North in the eastern theatre, and a ranger had one in his hand that had been recovered from a basket of a hot air balloon. I did not catch anything else he had to say about it.
With your explanation, I am assuming it is authenic.