Epidermal growth factor receptor (EGFR) is a key gene for diagnosing non-small cell lung cancer (NSCLC), which affects subsequent treatment arrangements. In clinical practice, compared with invasive testing, non-invasive detection of such genes can improve diagnostic efficiency and alleviate patient suffering. We propose a non-invasive decision-support method aimed at identifying EGFR mutations or wild type in NSCLC to avoid traumatic examination. To alleviate the inherent translational invariance of convolutional neural networks (CNNs) that results in the insufficiency to capture long-range dependencies, we propose a EGFR mutations or wild-type recognition method that combines CNNs with Transformers. In addition, we develop a lightweight dot-product strategy to address computational complexity, which not only reduces computational demands but also improves the interaction of image sequence information. The proposed method demonstrates superior performance, with an area under the curve of 88.56%, accuracy (ACC) of 83.17%, specificity (Spe) of 85.34%, and sensitivity (Sen) of 80.25%. In particular, the gradient-weighted class activation mapping analysis further shows that our algorithm more effectively concentrates on activation regions relevant to the predictions. The results of the experiments demonstrated that our proposed method is effective in distinguishing between EGFR mutations and wild type, showing superior classification performance compared with other methods. Notably, it introduces a non-invasive alternative for clinical examination, which is of considerable importance for the clinical diagnosis of NSCLC.