Communication systems operating in mixed white Gaussian and impulsive noise (IN) environments suffer from severe performance degradation, rendering conventional constellations suboptimal. In this paper, we propose a joint geometric and probabilistic shaping scheme designed to maximize the cutoff rate (CR) under such mixed noise conditions. Instead of relying on loose approximations, we derive rigorous closed-form lower and upper bounds for the CR. To overcome the analytical intractability of the integral terms, we develop a novel piecewise linear approximation that exploits the algebraic structure of the noise model, yielding tractable objectives for optimization. Subsequently, a projected gradient-based algorithm is employed to jointly optimize the constellation geometry and probability mass function. Numerical results demonstrate that our derived bounds are tight, and the proposed hybrid shaping scheme significantly outperforms conventional baseline schemes, especially when the input power is not large enough.