I bought a Lyman Kentucky pistol once with the intention of hunting deer. Then I found out is wasn't legal in Colorado. It didn't meet the minimum required fpe that Colorado specifies. After thinking about it. It really doesn't. Short barrel, and 40gr of powder is not a powerful load. Would you use that in a rifle to hunt deer?
So, i'd suggest at least a .54 cal, and as heavy a load of powder that the gun can shoot safely. Then get close, and only take solid double lung shots.
After finding out i couldn't shoot big game I used the gun for rabbits and squirrels. Quite a challenge to hit a running rabbit with the pistol. Mine was .50 cal.