In this paper, we propose p-Blend, an efficient and effective blendshape perturbation mechanism designed to defend against both intra- and cross-app re-identification attacks in virtual reality. p-Blend provides privacy protection when streaming blendshape data to third-party applications on VR devices. In its design, we consider both privacy and utility. p-Blend not only perturbs blendshape values to resist re-identification attacks but also preserves the smoothness of facial animations and the naturalness of facial expressions, ensuring the continued usability of the data. We validate the effectiveness of p-Blend through extensive empirical evaluations and user studies. Quantitative experiments on a large-scale dataset collected from 45 participants demonstrate that p-Blend significantly reduces re-identification accuracy across a range of machine learning models. While pure-random perturbation fails to prevent attacks that exploit statistical features, p-Blend effectively mitigates these risks in both raw and statistical blendshape data. Additionally, user study results show that facial animations generated from p-Blend-perturbed blendshapes maintain greater smoothness and naturalness compared to those using purely random perturbation. The codes and dataset are available at https://github.com/jingwei1016/p-Blend.