Protecting user data privacy can be achieved via many methods, from statistical transformations to generative models. However, all of them have critical drawbacks. For example, creating a transformed data set using traditional techniques is highly time-consuming. Also, recent deep learning-based solutions require significant computational resources in addition to long training phases, and differentially private-based solutions may undermine data utility. In this paper, we propose $ε$-PrivateSMOTE, a technique designed for safeguarding against re-identification and linkage attacks, particularly addressing cases with a high \sloppy re-identification risk. Our proposal combines synthetic data generation via noise-induced interpolation with differential privacy principles to obfuscate high-risk cases. We demonstrate how $ε$-PrivateSMOTE is capable of achieving competitive results in privacy risk and better predictive performance when compared to multiple traditional and state-of-the-art privacy-preservation methods, including generative adversarial networks, variational autoencoders, and differential privacy baselines. We also show how our method improves time requirements by at least a factor of 9 and is a resource-efficient solution that ensures high performance without specialised hardware.