Accurate pulse-oximeter readings are critical for clinical decisions, especially when arterial blood-gas tests - the gold standard for determining oxygen saturation levels - are not available, such as when determining COVID-19 severity. Several studies demonstrate that pulse oxygen saturation estimated from photoplethysmography (PPG) introduces a racial bias due to the more profound scattering of light in subjects with darker skin due to the increased presence of melanin. This leads to an overestimation of blood oxygen saturation in those with darker skin that is increased for low blood oxygen levels and can result in a patient not receiving potentially life-saving supplemental oxygen. This racial bias has been comprehensively studied in conventional finger pulse oximetry but in other less commonly used measurement sites, such as in-ear pulse oximetry, it remains unexplored. Different measurement sites can have thinner epidermis compared with the finger and lower exposure to sunlight (such as is the case with the ear canal), and we hypothesise that this could reduce the bias introduced by skin tone on pulse oximetry. To this end, we compute SpO2 in different body locations, during rest and breath-holds, and compare with the index finger. The study involves a participant pool covering 6-pigmentation categories from Fitzpatrick's Skin Pigmentation scale. These preliminary results indicate that locations characterized by cartilaginous highly vascularized tissues may be less prone to the influence of melanin and pigmentation in the estimation of SpO2, paving the way for the development of non-discriminatory pulse oximetry devices.