Fourier transform infrared (FTIR) spectroscopy is a highly versatile tool for cell and tissue analysis. Modern commercial FTIR microspectroscopes allow the acquisition of good-quality hyperspectral images from cytopathological samples within relatively short times. This study aims at assessing the abilities of FTIR spectra to discriminate different types of cultured skin cell lines by different computer analysis technologies. In particular, 22700 single skin cells, belonging to two non-tumoral and two tumoral cell lines, were analysed. These cells were prepared in three different batches that included each cell type. Different spectral preprocessing and classification strategies were considered, including the current standard approaches to reduce Mie scattering artefacts. Special care was taken for the optimisation, training and evaluation of the learning models in order to avoid possible overfitting. Excellent classification performance (balanced accuracy between 0.85 and 0.95) was achieved when the algorithms were trained and tested with the cells from the same batch. When cells from different batches were used for training and testing the balanced accuracy reached values between 0.35 and 0.6, demonstrating the strong influence of sample preparation on the results and comparability of cell FTIR spectra. A deep study of the most optimistic results was performed in order to identify perturbations that influenced the final classification.