The most appropriate next step in management is spirometry. This patient, who is a smoker with intermittent cough and dyspnea, likely has COPD. Although dyspnea, cough, and sputum production are characteristic symptoms of COPD, these symptoms can be variable and the cough can be nonproductive. This patient requires spirometry, which measures the FEV₁ and FVC, and the FEV₁/FVC ratio to assess for and quantify any degree of airflow obstruction present. Patients with COPD have a FEV₁/FVC ratio of less than or equal to 70%. Spirometry is reproducible and provides an objective measurement of airflow obstruction. Screening for COPD with spirometry in individuals without respiratory symptoms is not recommended, but it is indicated in this patient with symptoms and a suggestive clinical history for COPD.

CT scanning is used to evaluate parenchymal lung lesions (such as nodules) and other potential chest pathology (such as pleural or mediastinal disease). However, it is not effective in diagnosing COPD, particularly in this patient with a normal plain chest radiograph. In addition, guidelines recommend low-dose CT scanning for current or former smokers aged 55 to 80 years with a smoking history of at least 30-pack-years with no history of lung cancer; this patient does not fit these criteria.

Polysomnography is used for evaluation of suspected sleep-disordered breathing (such as sleep apnea). However, this patient does not have symptoms suggestive of sleep apnea or other sleep or nocturnal breathing disorders. Therefore, polysomnography is not indicated.

Although gastroesophageal reflux disease (GERD) is a common cause of chronic cough, and a trial of an empiric proton pump inhibitor is reasonable in patients with unexplained cough and otherwise negative evaluation, GERD would not account for this patient's dyspnea symptoms. Because his clinical presentation is more consistent with mild COPD, empiric treatment for GERD would not be the preferred next management step.