This paper presents results from the examination of a set of experimental samples using fibre optic reflectance spectroscopy (FORS) and diffuse reflectance imaging spectroscopy in the short-wave infrared (SWIR) range, combined with statistical analysis of the data for the discrimination and mapping of poppy and linseed oil. The aim was to evaluate the efficacy of this non-invasive approach for the study of paint samples with a view to the application of the method for characterisation of the two drying oils in painted art. The approach allowed discrimination between the two drying oils based on FORS spectra and the hyperspectral cube, indicating the influence of the spectral region around 1700 nm on the statistical discrimination based on the anti-symmetric and symmetric first overtone stretching of methylenic CH₂ groups. This method is being studied as a potential non-invasive method of organic analysis of oil types that have formerly been studied using gas chromatography-mass spectrometry (GC-MS), which requires micro-samples.