The gun is probably not rated for smokeless powder, so it would not be safe to shoot with store-bought ammo.
If you wanted to use it, or even just shoot it now and then, for sentimental reasons you could roll your own.
Its actually WAY easier than you may think. It would only cost you about $35 for a roll crimp tool and set of lee dippers. Once you purchased the shotshell components, you could load a few rounds with Pyrodex BP substitute (walmart) for very cheap.
Said shell would be just as effective now as they were on game in the early 1900's, and they wouldn't hurt your wallet.
This is provided the gun is still in good shape otherwise.