Deep Reinforcement Learning has achieved remarkable progress in solving NP-hard scheduling problems. However, existing methods primarily focus on optimizing average performance over training instances, overlooking the core objective of solving each individual instance with high quality. While several instance-wise adaptation mechanisms have been proposed, they are test-time approaches only and cannot share knowledge across different adaptation tasks. Moreover, they largely rely on gradient-based optimization, which could be ineffective in dealing with combinatorial optimization problems. We address the above issues by proposing an instance-wise meta-learning framework. It trains a meta model to acquire a generalizable initialization that effectively guides per-instance adaptation during inference, and overcomes the limitations of gradient-based methods by leveraging a derivative-free optimization scheme that is fully GPU parallelizable. Experimental results on representative scheduling problems demonstrate that our method consistently outperforms existing learning-based scheduling methods and instance-wise adaptation mechanisms under various task sizes and distributions.