Chaotic and hyperchaotic systems have been widely investigated for pseudorandom sequence generation and image encryption, but many existing approaches remain limited by relatively narrow parameter regions and predominantly classical dynamics. This study proposes a Quantum-Walk-Enhanced Cross-Coupled Hyperchaotic Map (QE-CCHM), a hybrid classical–quantum dynamical framework that introduces process innovation by integrating nonlinear cross-coupled classical states with two discrete-time quantum walks (DTQWs) through bidirectional measurement feedback. The quantum observables dynamically influence the classical states and the coin angles of the coupled DTQW subsystems, making quantum evolution an integral component of the dynamical process. The proposed system is evaluated using phase-space trajectories, bifurcation diagrams, Lyapunov exponents (LE), and broad parameter-domain exploration. In the investigated region 3.5≤ξ≤50, both leading LEs remain positive across all 100 evaluated parameter values, increasing from 6.2501 and 5.3408 at ξ=3.5 to 9.5432 and 8.6661 at ξ=50. A global exploration further investigates ξ from 10^-2 to approximately 10^308, including 10,033 evaluations across the extended positive-parameter domain. The resulting sequences exhibit high normalized entropy and low lag-1 autocorrelation across widely separated parameter scales. For application validation, the generated sequences are applied to a reversible image-encryption scheme combining pixel permutation and modular substitution. Across six grayscale images, entropy exceeds 7.998 bits/pixel, adjacent-pixel correlations approach zero, and NPCR and UACI range from 99.59% to 99.63% and 33.09% to 33.69%, respectively, demonstrating the potential of QE-CCHM for pseudo-random sequence generation and image encryption.