Feature sharing via split inference offers a lightweight alternative to federated learning for resource-constrained hospitals, but transmitted features still leak patient identity information and lack practical mechanisms for controlled feature sharing. We propose Keyed Nonlinear Transform (KNT), a drop-in feature transformation that applies key-conditioned obfuscation to intermediate representations. KNT reduces re-identification AUC from 0.635 to 0.586, corresponding to a 36% reduction in above-chance identity signal, while introducing only 0.15 ms CPU overhead, without backbone retraining, and preserving classification performance within 1.0 pp. Our analysis shows that KNT's nonlinear transform prevents closed-form inversion and shifts recovery to iterative gradient-based optimization under full key compromise, substantially increasing inversion difficulty. The same transform generalizes to dense prediction tasks, incurring only a 4.4 pp Dice reduction on skin-lesion segmentation without retraining. These results position KNT as a practical and efficient privacy layer for split inference deployments.