Accurate 3D modelling of grapevines is crucial for precision viticulture, particularly for informed pruning decisions and automated management techniques. However, the intricate structure of grapevines poses significant challenges for traditional skeletonization algorithms. This paper presents an adaptation of the Smart-Tree algorithm for 3D grapevine modelling, addressing the unique characteristics of grapevine structures. We introduce a graph-based method for disambiguating skeletonization. Our method delineates individual cane skeletons, which are crucial for precise analysis and management. We validate our approach using annotated real-world grapevine point clouds, demonstrating improvement of 15.8% in the F1 score compared to the original Smart-Tree algorithm. This research contributes to advancing 3D grapevine modelling techniques, potentially enhancing both the sustainability and profitability of grape production through more precise and automated viticulture practices