Background: Nitric oxide (NO) has been linked to the pathogenesis of asbestos-related pleural diseases, including an extremely aggressive cancer called malignant pleural mesothelioma (MPM). Given that MPM cells are characterized by a higher expression of NO synthases and elevated NO production relative to normal cells, the use of NO-donor compounds could potentially saturate the cancerous cells with NO, triggering their death. Methods: We developed a novel class of NO prodrugs by merging two NO-releasing components, 1,2,5-oxadiazole 2-oxides (furoxans) and 1,2,4-oxadiazoles, and studied their NO-releasing characteristics in a time-dependent manner using the Griess assay. The cytotoxicity against two human MPM cell lines and non-cancerous lung fibroblasts was evaluated using a colorimetric MTT assay. Results: All compounds exhibited excellent NO-donating properties, surpassing the capacity of two reference NO donor compounds, 3-carbamoyl-4-(hydroxymethyl)furoxan (CAS-1609) and 4-ethoxy-3-phenylsulphonylfuroxan (CHF-2363), by at least 1.5–3 times. All oxadiazole hybrids demonstrated high cytotoxicity against MPM cell lines in a low micromolar range, comparable or higher than the cytotoxicity of the standard-of-care drug cisplatin. Conclusions: Notably, the novel compounds displayed a markedly greater selectivity towards cancerous cells than cisplatin when compared with non-cancerous lung fibroblasts, aligning with the intended design.