“What types of masks are used for handing nuclear waste?”

Probably the best masks for dealing with radioisotopic contamination are similar to military "gas masks" including activated carbon filters. Since nuclear rays, particularly gamma rays are penetrating, masks alone are not sufficient to protect against all nuclear waste and maintaining short times of exposure and optimal, longer distances are also important. People involved in controlling nuclear waste from larger sources may use heavy metal shielding and also wear suits with their air supply specially filtered. Also monitoring of exposure in real time is important if larger amounts (or higher levels or radioactivity) of waste are involved.

Any materials to be shipped which are radioactive must be shipped in containers regulated by the Dept of Transportation so that nothing escapes into the environment to be inhaled.

Most nuclear waste does nor aerosolize. If there is aerosol formation the isotope is handled under a vacuum hood. Masks do not protect from radiation, but if it is tagges to particles a mask might work.