We introduce SpLap, a proxy-free deformation method for Gaussian splats (GS) based on a Laplacian operator computed from our novel surface-aware splat graph. Existing approaches to GS deformation typically rely on deformation proxies such as cages or meshes, but they suffer from dependency on proxy quality and additional computational overhead. An alternative is to directly apply Laplacian-based deformation techniques by treating splats as point clouds. However, this often fail to properly capture surface information due to lack of explicit structure. To address this, we propose a novel method that constructs a surface-aware splat graph, enabling the Laplacian operator derived from it to support more plausible deformations that preserve details and topology. Our key idea is to leverage the spatial arrangement encoded in splats, defining neighboring splats not merely by the distance between their centers, but by their intersections. Furthermore, we introduce a Gaussian kernel adaptation technique that preserves surface structure under deformation, thereby improving rendering quality after deformation. In our experiments, we demonstrate the superior performance of our method compared to both proxy-based and proxy-free baselines, evaluated on 50 challenging objects from the ShapeNet, Objaverse, and Sketchfab datasets, as well as the NeRF-Synthetic dataset. Code is available at https://github.com/kjae0/SpLap.