Cardiovascular diseases (CVDs), the leading cause of death worldwide, can be prevented in most cases through behavioral interventions. Therefore, effective communication of CVD risk and projected risk reduction by risk factor modification plays a crucial role in reducing CVD risk at the individual level. However, despite interest in refining risk estimation with improved prediction models such as SCORE2, the guidelines for presenting these risk estimations in clinical practice remained essentially unchanged in the last few years, with graphical score charts (GSCs) continuing to be one of the prevalent systems. This work describes the design and implementation of Petal-X, a novel tool to support clinician-patient shared decision-making by explaining the CVD risk contributions of different factors and facilitating what-if analysis. Petal-X relies on a novel visualization, Petal Product Plots, and a tailor-made global surrogate model of SCORE2, whose fidelity is comparable to that of the GSCs used in clinical practice. We evaluated Petal-X compared to GSCs in a controlled experiment with 88 healthcare students, all but one with experience with chronic patients. The results show that Petal-X outperforms GSC in critical tasks, such as comparing the contribution to the patient's 10-year CVD risk of each modifiable risk factor, without a significant loss of perceived transparency, trust, or intent to use. Our study provides an innovative approach to the visualization and explanation of risk in clinical practice that, due to its model-agnostic nature, could continue to support next-generation artificial intelligence risk assessment models.