Traditionally, the analysis of carbon monoxide poisoning levels in humans involves the use of laboratory equipment, a process demanding extensive research time and posing health risks due to potential blood contamination during sample collection. Moreover, commercial pulse oximeters may yield inaccurate information about arterial blood oxygen saturation due to the spectral similarities between oxyhemoglobin and carboxyhemoglobin. This paper introduces a calibration-free method based on two-wave photoplethysmography, utilizing paired linear regression for non-invasive oxygen saturation measurement. The selection of wavelengths for non-invasive carboxyhemoglobin measurement via multi-wavelength PPG methods is justified. A mathematical model for non-invasive measurement of carboxyhemoglobin in human arterial blood is developed based on three-wave PPG, with system calibration performed using changes in carboxyhemoglobin at wavelengths 568 nm and 660 nm. The design of the photoplethysmography system, the three-wave sensor, and the accompanying software for non-invasive oxyhemoglobin and carboxyhemoglobin measurement are detailed. The conducted studies on non-invasive oxygen saturation measurement reveal a significant correlation and accuracy in oxygen saturation determination compared to a commercial pulse oximeter. Additionally, investigations into non-invasive carboxyhemoglobin measurement showcase the proposed PPG method and system's capability to classify individuals as smokers or non-smokers based on their blood carbon monoxide levels.