Illuminant estimation aims to infer scene illumination from image measurements despite intrinsic ambiguities between surface reflectance and lighting. Most existing methods operate on trichromatic RGB images and are therefore fundamentally limited by the restricted spectral information available. Hyperspectral imaging provides a much richer representation of scene radiance and has the potential to alleviate these ambiguities. However, its high dimensionality poses computational and statistical challenges. In this work, we systematically study the effect of spectral dimensionality and representation choice on illuminant estimation performance using hyperspectral data. We adopt the practical and effective Color-by-Correlation (CbC) framework as the estimation backbone and analyze its behavior under different spectral dimensionality reduction strategies. Our results offer practical insights into how hyperspectral information can be efficiently exploited for illuminant estimation and identify conditions under which compact spectral representations outperform conventional RGB-based approaches. The code is available at https://github.com/IVRL/Reduced-Spectral-Color-Constancy.