Local carotid pulse wave velocity (cPWV), a hemodynamic variable related to arterial stiffness, is a recognized risk indicator for cardiovascular disease. Yet, current methods for its estimation pose challenges, requiring multiple simultaneous local measurements, as is the case for the established Bramwell-Hill (BH) method, or relying on assumptions that may not universally apply, as for single-measurement loop-based methods. This study introduces a novel, non-invasive, single-measurement method for estimating local cPWV. The proposed method relies solely on morphological indices derived from the carotid velocity waveform, measured via pulsed wave Doppler (pw-D) ultrasound. A multivariate regression (MVR) model relating eight such indices to cPWV was trained on a large available virtual cohort (N=5,160), previously generated via one-dimensional hemodynamic modeling. The MVR model was then tested on a clinical dataset of 27 cardiac surgery patients, showing moderate but significant correlation with the reference Bramwell-Hill method (r=0.54, p<0.01), and Bland-Altman values falling within clinically acceptable thresholds (mean difference 0.16 m/s, limits of agreement ±1.98 m/s). The proposed method outperformed the alternative pressure-less flow-area loop (QA-loop) method, which compared poorly to reference BH values (r=0.47, p<0.05, mean difference 0.72 m/s, and limits of agreement ±5.41 m/s). Furthermore, the proposed method showed the lowest intra-subject coefficient of variation (median 2.4%, interquartile range (IQR) 0-4.2%), and measurement-related uncertainty (median 0.11 m/s, IQR 0.07-0.23 m/s) among the three compared methods.