Hyperspectral imaging (HSI) systems collect both spatial (morphological) and spectral (chemical) information from a sample. HSI can provide sensitive analysis for biological and medical applications, for example, simultaneously measuring reflectance and fluorescence properties of a tissue, which together with structural information could improve early cancer detection and tumour characterisation. Illumination uniformity is a critical pre-condition for quantitative data extraction from an HSI system. Non-uniformity can cause glare, specular reflection and unwanted shading, which negatively impact statistical analysis procedures used to extract abundance of different chemical species. Here, we model and evaluate several illumination systems frequently used in wide-field biomedical imaging to test their potential for HSI. We use the software LightTools and FRED. The analysed systems include: a fibre ring light; a light emitting diode (LED) ring; and a diffuse scattering dome. Each system is characterised for spectral, spatial, and angular uniformity, as well as transfer efficiency. Furthermore, an approach to measure uniformity using the Kullback-Leibler divergence (KLD) is introduced. The KLD is generalisable to arbitrary illumination shapes, making it an attractive approach for characterising illumination distributions. Although the systems are quite comparable in their spatial and spectral uniformity, the most uniform angular distribution is achieved using a diffuse scattering dome, yielding a contrast of 0.503 and average deviation of 0.303 over a ±60° field of view with a 3.9% model error in the angular domain. Our results suggest that conventional illumination sources can be applied in HSI, but in the case of low light levels, bespoke illumination sources may offer improved performance.