In finite element simulations of structural dynamics, the stability of conditionally stable time integration schemes is governed by the critical time step. Although exact stability limits can be obtained through eigenvalue analysis, this approach is computationally impractical for large-scale models. Consequently, practical simulations rely on heuristic, element-level estimates that are often inaccurate and may become non-conservative, especially for distorted element geometries. Recent studies have shown that more accurate time step estimators can be derived using machine learning to exploit the discrete representation of all possible element configurations (Willmann et al. (2025)). While the preceding contribution (Schilling et al. (2026)) focused on their practical integration into relevant engineering simulations and their extension to non-local approaches, taking into account information of neighboring elements, this study addresses the choice of suitable input parameters for data-based time step estimators. Parameters with an analytically known influence on the critical time step are separated from parameters whose influence is computationally expensive to evaluate and therefore requires estimation. For simple material laws, this separation is straightforward for material parameters. While the influence of the element size on the critical time step is analytically known, the effect of the element shape is not available in closed form and must therefore be estimated. This study investigates two different sets of parameters to describe the shape of quadrilateral elements with regard to their suitability as inputs for machine learning methods. One description is based on nodal coordinates, see Willmann et al. (2025), whereas the other employs a newly formulated set of geometrically interpretable shape parameters that quantify deviations from a unit square. We analyze how the shape representation affects the predictive performance of data-based time step estimators and whether shape parameters can reduce the required training data while maintaining accuracy. This is particularly relevant for extensions to higher-dimensional problems. Moreover, the proposed parametrization may improve the explainability of the learned model. We gratefully acknowledge the support for this research from the German Research Foundation (DFG), Research Grant BI 722/15-1.