What health-hazard are you concerned about?

If it is lead, then please understand that I have been reloading (and processing the brass to do so) for 40 years. I have dry tumbled with walnut shells, wet tumbled with metal pins, soaked in weak acid solutions, as well as both dry and/or wet tumbled in mica, ball bearings, and rice. Regardless of the method, I have never taken any specific precautions to mitigate exposure to the tumbling media or any contaminants that might be in it, including lead.

Also, for the last 30 years, I have lived within sight of what was once one of the largest lead smelters in Texas. Because I live so close to a source of lead "contamination", I am regularly tested for lead both in my blood and in my hair.

Even with all that lead exposure, the lab tests continue to come back showing no detectable levels of lead. Based on my experience, you should choose a method for tumbling that produces the results you find pleasing with a level of effort that you find acceptable without worrying about exposure to lead or other toxins.