Polarization probes of new physics in lepton-flavor-violating hyperon production from <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>e</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:mi>N</mml:mi><mml:mo stretch

While charged lepton-flavor-violating tau decays to strange mesons provide powerful probes of the underlying <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>τ</a:mi><a:mo stretchy="false">→</a:mo><a:mo>ℓ</a:mo><a:mi>d</a:mi><a:mover accent="true"><a:mi>s</a:mi><a:mo stretchy="false">¯</a:mo></a:mover></a:math> transition, the corresponding decay modes involving hyperons are kinematically forbidden. To address this gap, we propose the quasielastic scattering processes <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:msup><f:mi>e</f:mi><f:mo>−</f:mo></f:msup><f:mi>N</f:mi><f:mo stretchy="false">→</f:mo><f:msup><f:mi>τ</f:mi><f:mo>−</f:mo></f:msup><f:mi>Y</f:mi></f:math>. Within a general low-energy effective Lagrangian, we perform a comprehensive analysis of the final-state polarizations of both the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>τ</i:mi></i:math> lepton and the hyperon <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>Y</k:mi></k:math>, systematically addressing the theoretical uncertainty driven by the model dependence of form factors. Our analysis demonstrates that while this uncertainty leads to large variations in predicted rates, the polarization observables can potentially distinguish between the form factor models, and help to determine the chiral nature of the vectorial new physics interaction. Finally, we forecast the event rates for future facilities, revealing a strong dependence on the form factor models, with predicted yields ranging from potentially observable levels to rates far below current detection thresholds.