Electrodermal activity (EDA) is widely used in wearable Internet of Medical Things (IoMT) systems for continuous health monitoring, including autonomic assessment. However, EDA signals are highly vulnerable to motion artifacts and environmental noise, limiting reliable deployment in harsh operating conditions such as underwater. This study proposes a robust, deployable EDA denoising framework that generalizes across multiple measurement locations and harsh environments. The framework integrates a hybrid CNN-Transformer teacher model with a lightweight depth-wise separable CNN student model via a knowledge distillation (KD) strategy. To further improve robustness, a realistic data augmentation scheme is introduced to simulate diverse motion artifacts and environmental distortions. The KD-based student model significantly reduces model size (7.87 MB to 0.51 MB) and computational cost (105.1M to 11.61M FLOPs) while maintaining denoising performance (MAE: 0.144, SNR improvement: 12.08 dB) using the public dataset validation. In real-world underwater conditions (UMAC dataset) testing, the proposed method substantially improves skin conductance response reconstruction, reducing mean absolute error from 2.809 to 0.215. Furthermore, on independent testing using the CNS-OT dataset, the denoised signals enhanced downstream CNS-OT prediction performance, achieving the highest AUROC (0.806) compared to prior denoising methods. The proposed method also improved the early prediction rate (sensitivity) from 0.550 to 0.767, enabling CNS-OT prediction up to a median of 6.9 minutes before symptom onset. These results demonstrate that the proposed framework not only improves EDA signal quality but also enhances clinically relevant prediction performance while remaining suitable for deployment in resource-constrained wearable Internet of Things systems operating in harsh environments.