Audio classification tasks based on deep learning methods are increasingly being performed on edge devices. This offers advantages such as reduced latency, lower bandwidth usage, and enhanced privacy. However, implementing audio classification on edge devices presents challenges due to limited memory, processing power, and energy constraints. In this paper, we focus on ultra-low-power microcontroller units (MCUs). We present a novel state-of-the-art neural network model based on MobileNetV4 for urban sound classification. It is optimized for deployment on resource-constrained MCUs by (a) adapted quantization-aware training techniques to reduce model size and inference latency, and (b) offline knowledge distillation with attention-based teacher models to enhance performance. We deploy our trained model on an Expressif ESP32-S3 MCU and present experimental results for several datasets. The final deployed model can be used to classify 77 urban sounds on an ESP32-S3. Our work represents the first application of the MobileNetV4 architecture for urban sound classification on the ESP32-S3 hardware.