There might be a way to handle the damage inflicted on the animal in particular, or as mentioned lower the health. I would expect a headshot or center mass shot be sufficient to take down a small-medium mammal.
Disagree with removing hunting as a whole (appreciate that's not the original suggestion, but was mentioned). This is a career most characters take. Because the weapons are misused for criminal activity to me seems a bit of an over reaction to scrap the job completely!