This paper investigates three TinyML models (including a novel one, entitled HVTINY), and compares them against state-of-the-art solutions for the problem of skin cancer detection and diagnosis. Results presented herein indicate that such compact models fit well into low cost, portable MCU-based platforms like ESP32-CAM, thus ensuring a cheap and convenient solution to build portable medical devices for early screening in primary care or remote areas. The results for some widely know datasets (a binary one, for detecting malign lesions and a dataset for diagnosis classification) indicates state of the art performance (93% accuracy for malign lesion detection, and more than 98% for skin-lesions classification) comparable to what is obtainable with more complex models, associated with more costly medium size computational platforms.