Skin cancer is frequently occurring and has become a major contributor to both cancer incidence and mortality. Accurate and timely diagnosis of skin cancer holds the potential to save lives. Deep learning-based methods have demonstrated significant advancements in the screening of skin cancers. However, most current approaches rely on a single modality input for diagnosis, thereby missing out on valuable complementary information that could enhance accuracy. Although some multimodal-based methods exist, they often lack adaptability and fail to fully leverage multimodal information. In this paper, we introduce a novel uncertainty-based hybrid fusion strategy for a multi-modal learning algorithm aimed at skin cancer diagnosis. Our approach specifically combines three different modalities: clinical images, dermoscopy images, and metadata, to make the final classification. For the fusion of two image modalities, we employ an intermediate fusion strategy that considers the similarity between clinical and dermoscopy images to extract features containing both complementary and correlated information. To capture the correlated information, we utilize cosine similarity, and we employ concatenation as the means for integrating complementary information. In the fusion of image and metadata modalities, we leverage uncertainty to obtain confident late fusion results, allowing our method to adaptively combine the information from different modalities. We conducted comprehensive experiments using a popular publicly available skin disease diagnosis dataset, and the results of these experiments demonstrate the effectiveness of our proposed method. Our proposed fusion algorithm could enhance the clinical applicability of automated skin lesion classification, offering a more robust and adaptive way to make automatic diagnoses with the help of uncertainty mechanism. Code is available at https://github.com/Zuo-Lihan/CosCatNet-Adaptive_Fusion_Algorithm.