Modern logistics networks generate rich operational data streams at every warehouse node and transportation lane -- from order timestamps and routing records to shipping manifests -- yet predicting delivery delays remains predominantly reactive. Existing predictive approaches typically treat this problem either as a tabular classification task, ignoring network topology, or as a time-series anomaly detection task, overlooking the spatial dependencies of the supply chain graph. To bridge this gap, we propose a hybrid deep learning framework for proactive supply chain risk management. The proposed method jointly models temporal order-flow dynamics via a lightweight Transformer patch encoder and inter-hub relational dependencies through an Edge-Aware Graph Attention Network (E-GAT), optimized via a multi-task learning objective. Evaluated on the real-world DataCo Smart Supply Chain dataset, our framework achieves consistent improvements over baseline methods, yielding an F1-score of 0.8762 and an AUC-ROC of 0.9773. Across four independent random seeds, the framework exhibits a cross-seed F1 standard deviation of only 0.0089 -- a 3.8 times improvement over the best ablated variant -- achieving the strongest balance of predictive accuracy and training stability among all evaluated models.