A disposable safety scalpel comprises a handle and a blade carrier, which fit together such that the blade carrier can shift between a retracted position whereby a front portion of the handle covers or otherwise blocks contact with the sharp edge of the blade, and an extended position whereby the sharp edge of the blade protrudes beyond the handle. The handle has a substantially flat base portion that can be held by the forefinger of the surgeon for shifting of the carrier with the thumb between retracted and extended positions. When the carrier and blade are extended, the surgeon can hold only the base of the handle between the thumb and forefinger for cutting during surgery. The shifting between the retracted and deployed positions with only the fingers of one hand can be readily accomplished even in the presence of slippery fluids during surgery.