During yield operations, the materials within the National Ignition Facility (NIF) cryogenic target positioner will be exposed to high fluences of high-energy neutrons. If left unchecked, these neutrons could deposit unacceptably high amounts of energy within the cryogenic fluids. In addition, these neutrons will induce residual radioactivity within the target positioner and may lead to intolerable dose rates for maintenance personnel. Through careful design and selection of materials, however, these effects may be mitigated. The present work uses nominal design characteristics for the cryogenic target positioner to show that traditional cryogenic and structural materials will not produce an acceptable design. Further, we develop an alternate design that addresses the issues of neutron shielding and activation.