Calisthenics skill classification is the computer vision task of inferring the skill performed by an athlete from images, enabling automatic performance assessment and personalized analytics. Traditional methods for calisthenics skill recognition are based on pose estimation methods to determine the position of skeletal data from images, which is later fed to a classification algorithm to infer the performed skill. Despite the progress in human pose estimation algorithms, they still involve high computational costs, long inference times, and complex setups, which limit the applicability of such approaches in real-time applications or mobile devices. This work proposes a direct approach to calisthenics skill recognition, which leverages depth estimation and athlete patch retrieval to avoid the computationally expensive human pose estimation module. Using Depth Anything V2 for depth estimation and YOLOv10 for athlete localization, we segment the subject from the background rather than relying on traditional pose estimation techniques. This strategy increases efficiency, reduces inference time, and improves classification accuracy. Our approach significantly outperforms skeleton-based methods, achieving 38.3x faster inference with RGB image patches and improved classification accuracy with depth patches (0.837 vs. 0.815). Beyond these performance gains, the modular design of our pipeline allows for flexible replacement of components, enabling future enhancements and adaptation to real-world applications.