Dynamic signed networks (DSNs) are common in online platforms, where time-stamped positive and negative relations evolve over time. A core task in DSNs is dynamic edge prediction, which forecasts future relations by jointly modeling edge existence and polarity (positive, negative, or non-existent). However, existing dynamic signed network embedding (DSNE) methods often entangle positive and negative signals within a shared temporal state and rely on node-specific temporal trajectories, which can obscure polarity-asymmetric dynamics and harm inductive generalization, especially under cold-start evaluation. We study an inductive setting where each test edge contains at least one endpoint node held out from training, while its interactions prior to the prediction time are available as historical evidence. The model must therefore infer representations for unseen nodes solely from such limited history. We propose IDP-DSN, an Inductive Dual-Polarity framework for Dynamic Signed Networks. IDP-DSN maintains sign-selective memories to model positive and negative temporal dynamics separately, performs history-only neighborhood inference for unseen nodes (instead of learned node-wise trajectories), and enforces polarity-wise static--dynamic disentanglement via an orthogonality regularizer. Experiments on BitcoinAlpha, BitcoinOTC, Wiki-RfA, and Epinions demonstrate consistent improvements over the strongest baselines, achieving relative Macro-F1 gains of 16.8/23.4%, 16.9/24%, 30.1/25.5%, and 18.7/28.9% in the transductive/inductive settings, respectively. These results highlight the effectiveness of IDP-DSN on DSNs, particularly under inductive cold-start evaluation for dynamic signed edge prediction.