Chronic wounds affect the lives of millions of individuals globally, and due to substantial medical costs, treating chronic injuries is very challenging for the healthcare system. The classification of regular wound type is essential in wound care management and diagnosis since it can assist clinicians in deciding on the appropriate treatment method. Hence, an effective wound diagnostic tool would enable clinicians to classify the different types of chronic wounds in less time. The majority of the existing chronic wound classification methods are mainly focused on the binary classification of the wound types. A few approaches exist that classify chronic wounds into multiple classes, but these achieved lower performances for pressure and diabetic wound classification. Furthermore, cross-corpus evaluation is absent in chronic wound type classification, in order to better evaluate the efficacy of existing methods on real-time wound images. To address the limitations of the current studies, we propose a novel Swish-ELU EfficientNet-B4 (SEEN-B4) deep learning framework that can effectively identify and classify chronic wounds into multiple classes. Moreover, we also extend the existing Medetec and Advancing the Zenith of Healthcare (AZH) datasets to deal with the class imbalance problem of these datasets. Our proposed model is evaluated on publicly available AZH and Medetec datasets and their extended versions. Our experimental results indicate that the proposed SEEN-B4 model has attained an accuracy of 87.32%, 88.17%, 88%, and 89.34% on the AZH, Extended AZH, Medetec, and Extended Medetec datasets, respectively. We also show the effectiveness of our method against the existing state-of-the-art (SOTA) methods. Furthermore, we evaluated the proposed model for the cross-corpora scenario to demonstrate the model generalization aptitude, and interpret the model’s result through explainable AI techniques. The experimental results show the proposed model’s effectiveness for classifying chronic wound types.