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Several optical imaging techniques have been developed to ease the burden of skin cancer disease on our health care system. Hyperspectral images can be used to identify biological tissues by their diffuse reflected spectra. In this second part of a three-phase pilot study, we used a novel hand-held SICSURFIS Spectral Imager with an adaptable field of view and target-wise selectable wavelength channels to provide detailed spectral and spatial data for lesions on complex surfaces. The hyperspectral images (33 wavelengths, 477-891 nm) provided photometric data through individually controlled illumination modules, enabling convolutional networks to utilise spectral, spatial, and skin-surface models for the analyses. In total, 42 lesions were studied: 7 melanomas, 13 pigmented and 7 intradermal nevi, 10 basal cell carcinomas, and 5 squamous cell carcinomas. All lesions were excised for histological analyses. A pixel-wise analysis provided map-like images and classified pigmented lesions with a sensitivity of 87% and a specificity of 93%, and 79% and 91%, respectively, for non-pigmented lesions. A majority voting analysis, which provided the most probable lesion diagnosis, diagnosed 41 of 42 lesions correctly. This pilot study indicates that our non-invasive hyperspectral imaging system, which involves shape and depth data analysed by convolutional neural networks, is feasible for differentiating between malignant and benign pigmented and non-pigmented skin tumours, even on complex skin surfaces.