Obstructive sleep apnea (OSA) is a high-incidence disease that is seriously harmful and potentially dangerous. The objective of this study was to develop a noncontact sleep audio signal-based method for diagnosing potential OSA patients, aiming to provide a more convenient diagnostic approach compared to the traditional polysomnography (PSG) testing. The study employed a shifted window transformer model to detect snoring audio signals from whole-night sleep audio. First, a snoring detection model was trained on large-scale audio datasets. Subsequently, the deep feature statistical metrics of the detected snore audio were used to train a random forest classifier for OSA patient diagnosis. Using a self-collected dataset of 305 potential OSA patients, the proposed snore shifted-window transformer method (SST) achieved an accuracy of 85.9%, a sensitivity of 85.3%, and a precision of 85.6% in OSA patient classification. These values surpassed the state-of-the-art method by 9.7%, 10.7%, and 7.9%, respectively. The experimental results demonstrated that SST significantly improved the noncontact audio-based OSA diagnosis performance. The study's findings suggest a promising self-diagnosis method for potential OSA patients, potentially reducing the need for invasive and inconvenient diagnostic procedures.