Timely and accurate diagnosis is crucial in addressing the global rise in thyroid cancer, ensuring effective treatment strategies and improved patient outcomes. We present an intelligent classification method that couples an Adaptive Convolutional Neural Network (CNN) with Cohen-Daubechies-Feauveau (CDF9/7) wavelets whose detail coefficients are modulated by an n-scroll chaotic system to enrich discriminative features. We evaluate on the public DDTI thyroid ultrasound dataset (n = 1,638 images; 819 malignant / 819 benign) using 5-fold cross-validation, where the proposed method attains 98.17% accuracy, 98.76% sensitivity, 97.58% specificity, 97.55% F1-score, and an AUC of 0.9912. A controlled ablation shows that adding chaotic modulation to CDF9/7 improves accuracy by +8.79 percentage points over a CDF9/7-only CNN (from 89.38% to 98.17%). To objectively position our approach, we trained state-of-the-art backbones on the same data and splits: EfficientNetV2-S (96.58% accuracy; AUC 0.987), Swin-T (96.41%; 0.986), ViT-B/16 (95.72%; 0.983), and ConvNeXt-T (96.94%; 0.987). Our method outperforms the best of these by +1.23 points in accuracy and +0.0042 in AUC, while remaining computationally efficient (28.7 ms per image; 1,125 MB peak VRAM). Robustness is further supported by cross-dataset testing on TCIA (accuracy 95.82%) and transfer to an ISIC skin-lesion subset (n = 28 unique images, augmented to 2,048; accuracy 97.31%). Explainability analyses (Grad-CAM, SHAP, LIME) highlight clinically relevant regions. Altogether, the wavelet-chaos-CNN pipeline delivers state-of-the-art thyroid ultrasound classification with strong generalization and practical runtime characteristics suitable for clinical integration.