Existing 3D Gaussian Splatting (3DGS) methods for hand rendering rely on rigid skeletal motion with an oversimplified non-rigid motion model, which fails to capture fine geometric and appearance details. Additionally, they perform densification based solely on per-point gradients and process poses independently, ignoring spatial and temporal correlations. These limitations lead to geometric detail loss, temporal instability, and inefficient point distribution. To address these issues, we propose HandSplat, a novel Gaussian Splatting-based framework that enhances both fidelity and stability for hand rendering. To improve fidelity, we extend standard 3DGS attributes with implicit geometry and appearance embeddings for finer non-rigid motion modeling while preserving the static hand characteristic modeled by original 3DGS attributes. Additionally, we introduce a local gradient-aware densification strategy that dynamically refines Gaussian density in high-variation regions. To improve stability, we incorporate pose-conditioned attribute regularization to encourage attribute consistency across similar poses, mitigating temporal artifacts. Extensive experiments on InterHand2.6M demonstrate that HandSplat surpasses existing methods in fidelity and stability while achieving real-time performance. We will release the code and pre-trained models upon acceptance.