Access to real clinical data is heavily restricted by privacy regulations, hindering both healthcare research and education. These constraints slow progress in developing new treatments and data-driven healthcare solutions, while also limiting students' access to real-world datasets, leaving them without essential practical skills. High-utility synthetic datasets are therefore critical for advancing research and providing meaningful training material. However, current generative models -- such as Variational Autoencoders (VAEs) and Generative Adversarial Networks (GANs) -- produce surface-level realism at the expense of healthcare utility, blending distinct patient profiles and producing synthetic data of limited practical relevance. To overcome these limitations, we introduce CK4Gen (Cox Knowledge for Generation), a novel framework that leverages knowledge distillation from Cox Proportional Hazards (CoxPH) models to create synthetic survival datasets that preserve key clinical characteristics, including hazard ratios and survival curves. CK4Gen avoids the interpolation issues seen in VAEs and GANs by maintaining distinct patient risk profiles, ensuring realistic and reliable outputs for research and educational use. Validated across four benchmark datasets -- GBSG2, ACTG320, WHAS500, and FLChain -- CK4Gen outperforms competing techniques by better aligning real and synthetic data, enhancing survival model performance in both discrimination and calibration via data augmentation. As CK4Gen is scalable across clinical conditions, and with code to be made publicly available, future researchers can apply it to their own datasets to generate synthetic versions suitable for open sharing.