Physics-based Patient-Specific Biomechanical models (PSBMs), particularly those using finite element methods (FEM), simulate organ behaviors accurately but are computationally intensive, especially for hyper-elastic tissues. To address this, U-Mesh \cite{Mendizabal2020} introduced a data-driven approach using U-Net architecture, achieving real-time inference but reliant on precise stiffness knowledge at training. This paper introduces HyperU-Mesh, an extension that integrates a Hypernetwork to condition U-Mesh based on stiffness prior distributions. By training with FEM-simulated data that varies stiffness under a predefined distribution, HyperU-Mesh ensures accuracy across variable stiffness without retraining. Experimental results highlight its effectiveness across different scenarios, showing comparable accuracy to FEM while significantly improving speed.