For the detection of vocal-fold related pathologies, non-invasive modalities such as Electroglottographic (EGG) and speech signal analysis are very important. In this context, conventional features estimated using linear methods have always limitation in identifying the nonlinear dynamic variations inherent to vocal fold vibrations. This includes aperiodicity, cycle-to-cycle irregularity, and nonlinear vibratory behavior frequently seen in disordered phonation. Although recent models have shown improved classification performance, these methodologies generally require large, well-balanced datasets. Moreover, they provide limited interpretability of their acquired representations. Hence, we present a recurrence plot (RP) based framework to characterize three vocal pathologies such as Hyperfunctional Dysphonia (HFD), Laryngitis, and Vocal Polyps. RPs depict state-space evolution and show recurring structures linked to different regimes such as periodic, quasi-periodic, and irregular oscillatory nature. Recurrence Quantification Analysis (RQA) offers a collection of numerical metrics that define structural stability and variability in a mathematically rigorous way. The proposed method provides an interpretable and computationally efficient method for the objective evaluation of vocal fold disease by integrating recurrence-based modeling with supervised classification. Classification using a Random Forest model achieved high overall performance, showing an average testing accuracy of 81.58% for HFD and 79.61% for Laryngitis.