There's a very important point getting missed in this discussion:
Metallic lead is completely different from lead oxides and vapors. I am no expert on this but I have done a lot of research on the matter consulting a vast number of sources. My former business required that I comply with all OSHA/MSHA regulations for every type of industrial/commercial business I dealt with.
First things first - shooting a critter with a lead projectile does not make for lead oxide or lead vapors, the displaced lead of the projectile remains in its metallic form. If you ingest metallic lead, it will pass through your system and out the waste vent without incident unless it's sharp/pointed and causes some type of mechanical damage such as a cut or perforation within the intestinal tract.
Lead oxide is the toxin, this is what's contained in lead-base paint and similar coating products - the white powdery substance covering metallic lead - "white lead" sold for use as an oil drying agent.
The vapors (free molecules) or airborne dust given off by overheating, boiling, sanding or grinding metallic lead are brought into the body primarily via the lungs where it transfers to the bloodstream.
The lead solvents, such as those used to clean guns, are a problem as the solvents becomes the skin penetrating carrier bringing lead into the bloodstream.
I have been handling used lead and casting since I was knee-high to a grasshopper and while my old man didn't know or care about exposure to lead dust/vapors, chopping up corroded old lead pipes and casting was done in an enclosed basement for many years. As time went on and I learned about the potential dangers, I used an exhaust fan to keep the fumes out of my face. The most important things you can do when casting are:
Don't make dust. Don't stick your fingers in your mouth/eyes/nose. Don't stick your face over the pot. Don't overheat the melt. Wash your body and your clothes without dragging lead dust/oxides through the house. Not only for exposure but also for safety reasons, cover all exposed skin with non-flammable & non-melting clothing. Common sense goes a long way, there's plenty of information and equipment available these days so there's no reason why casting cannot be done safely by anyone wishing to do so.
I've gone through several full-body scans and heavy metal tests related to my work. No problem with lead at all but let me tell you, if you're worried about lead, do yourself a favor and worry more about zinc because it's a helluva lot more toxic and dangerous than lead! Ask me, I know. Once you get zinc poisoning, it never really goes away. You'll get so sick of chugging down buttermilk, you'll never want to see it again as long as you live and even the slightest exposure to zinc in other than solid form will bring on an almost instant relapse. I've burned tons of welding wire & stick electrode, welding/cutting fumes are a whole lot more dangerous than casting lead. BTW, two hours of exposure to city traffic puts more toxins in your body than a year's worth of bullet casting done right.
Below were pulled from two different sources - it's just basic information but perhaps it will help clarify a few things but most importantly, use common sense.
The leading cause of lead poisoning in adults is through inhalation of lead dust or lead vapor and through skin contact while working with certain chemicals and solvents. Lead dissolved in chemicals or solvents, enters the bloodstream primarily through exposed skin coming in contact with the chemical or solvent and is distributed to all tissues throughout the body via the bloodstream. The mean life of lead vapors is extremely short since they will: condense in the nuclei which are unstable and transform into smoke; rapidly react with oxygen forming lead oxide fumes which may contain strings of submicron particles; attach to the surface of or be absorbed within other dust particles. Lead vapors and aerosols remain in the airborne for a very short period of time as compared to other airborne contaminants. People within very close proximity to the source, or within a strong downstream airflow, of airborne lead are most at risk of inhalation exposure and at a moderate risk of ingestion exposure. Use of a mouth and nose respirator in combination with lead dust approved eye protection or the use of a full-face respirator, both utilizing lead vapor/dust filters, will reduce the likelihood of lead inhalation/ingestion to near zero provided proper decontamination methods are followed before removing protective equipment.
Mitigating the risks of poisoning via airborne lead hazards is both simple and cost effective as it requires little more than properly filtered full-face respirator combined with a basic washdown decontamination area for workers. Before leaving the contaminated area, workers enter a suitable decontamination chamber where all clothing is removed and placed into lidded solid container or covered bag. Worker then enters the washdown area to fully shower with soap prior to removing respirator. Upon removal of respirator, worker is to remove the outer particulate filter placing it into a covered container within the washdown chamber then use soap to thoroughly wash and rinse respirator assembly before repeating the personal washdown the process. Where a large volume of workers are involved, a method of passing contaminated respirators from the washdown chamber to a separate cleaning room should be employed so as to expedite the flow of workers through the washdown chamber. Soiled clothing should be thoroughly wetter to saturation before removing from container or bag for washing. All drains from washdown, decontamination and laundering areas should be fitted with removable lead filter traps to facilitate proper recycling or disposal. Worker's adherence to proper personal protective and decontamination procedures have proven 99.99% effective at mitigating exposure to lead.