Artificial Intelligence (AI) is advancing Teledermatology by complementing its features with intelligent skin diagnosis to support medical experts. Most of the skin diagnosis prediction models utilize the deep learning approach in the context of data-driven modeling. It faces challenging issues in deploying the model into low-resource devices such as mobile devices, as these models require high computational resources. Several research has focused on tiny AI models in edge computing frameworks to enhance accuracy retention upon deployment. One of the AI modeling framework approaches for low-resource devices is model compression. This study evaluates the efficiency of three AI model compression methods by assessing the diagnosis performance on mobile phone devices. The simulation shows that no model compression excels in all performance metrics. However, knowledge distillation stands out by not only retaining accuracy but also showing a 2.65% improvement over the baseline model, while providing the fastest inference speed of 109 ms.