Supplemental oxygen is not expected to improve cyanosis in this case.
Peripheral cyanosis is defined as cyanosis of the extremities and nail beds. It can be caused by peripheral arterial occlusion (as in the above patient), vasoconstriction, decreased peripheral blood flow, or abnormally large extraction of oxygen from normally saturated arterial blood.
Cyanosis secondary to vascular occlusion (the above patient) is not expected to improve either with warming or supplemental oxygen because blood is still not perfusing that extremity. Vasodilators are also not standard treatment for acute arterial occlusion.
Both warming and vasodilators such as calcium channel blockers have been used in the treatment of Raynaud’s Phenomenon, a form of peripheral cyanosis secondary to vasospasm of small arteries.
References:
Fernandez-Frackelton M. Cyanosis. In Marx JA, et al. Rosen’s Emergency Medicine. 8th ed. 2014. Chapter 14, 129-134.e1.
Sarko J, Stapczynski JS. Respiratory Distress. In Tintinalli JE, et al Tintinalli’s Emergency Medicine: A Comprehensive Study Guide. 7th edition. 2011. Chapter 65, 465-473.