Research and development of Li-Fi (Light Fidelity) in Internet-of-things (IoT) has created significant interest among researchers. The low-cost version of standard color shift keying (CSK) modulation scheme having single photodetector (PD) at the receiver can become an alternative to on-off keying (OOK) in IoT sensor networks as an M-ary CSK modulation scheme provides log 2 M times more data rate than that of OOK. This work revolves around optimizing the constellation points of single PD based CSK (CSK-1PD) to achieve a more power-efficient modulation scheme. The optimization has been done with and without average white tone constraint for uniform and non-uniform (exponential, Maxwell-Boltzmann, Pareto) source distributions. The constellation design strategy is based on maximizing the minimum distance among the differently distributed symbols. In the case of non-uniform distributions, the constellations points have been optimized by geometrically shaping the points based on their probabilistic shaping (PS). The optimized constellation points (OCPs) of CSK-1PD without white tone constraint provide higher signal-tonoise ratio (SNR) gain at forward error correction (FEC) limit symbol error rate (SER) as compared with strict white tone constraint. Further, the strict white tone constraint has been relaxed by considering the whole white light region in the CIE 1931 chromaticity diagram as white tone. The OCPs for uniform data with relaxed white tone constraint achieves SNR gain similar to without white tone constraint. However, for probabilistically shaped symbols, the SNR gain achieved from OCPs improves from strict white tone constraint but remains less than the without white tone constraint. A novel method to utilize an additional RGB LED at the transmitter side has been proposed and designed to maintain any white tone light in the white light region without degrading the maximum achieved SNR gain.