With old ammunition, you still have to be careful. Unless it was poorly manufactured, the seal between the bullet and the casing should still be intact which means the powder is still dry and capable of exploding. The primers used were typically mercury fulmanate and while they will deteriorate over time, they should all be considered as live and capable of igniting the powder if struck hard enough and in the right place. The nature of the primer and the positioning of it make it difficult for it to be struck in such a manner as to fire and set off the powder but it can happen. You could have two rounds together and the nose of one bullet gets driven into the primer of the other. Certain shells had a very pointed nose and would certainly be capable of imitating a firing pin. There could be a rock, nail, or other sharp object that could do the same. Is it likely to be arranged that way? No. Could they be? Yes. While it takes a pretty powerful blow, it can happen. So, IMHO, it boils down to reward versus risk. If you like to dig in those areas that still contain live ammunition and are willing to suffer the consequences if the unlikely happens, then you may possibly suffer some damage or someone in your party may be an innocent bystander as you dig them out. If, on the other hand, you can find other places to hunt that are not contaminated with live rounds, you can avoid most of the danger. Just remember that no battlefield is safe. There are other things that might be there that are much more dangerous and much more destructive than old bullets. Just because there are no bullets, that doesn't mean there isn't a mortar shell or a land mine. Still active after all these years.
For me, I'd rather dig somewhere else completely and buy any artifacts I just had to have.
Daryl