Sensing skins about 1.5 μm thick made of 40 nanolayers of conductive polymer nanocomposites (CPC) were sprayed layer by layer (sLbL) directly on a PET woven textile to demonstrate their versatility to monitor the deformation of a flexible, rigid and rough substrate such as a commercial boat sail. CPC sensing skins were developed by structuring a 3D carbon nanotubes network into three kinds of amorphous thermoplastic matrices (PMMA, aPS, PC). Adjustable parameters such as the thickness (number of sprayed layers) and the initial resistance of CPC transducers (CNT content relatively to percolation threshold) enabled to tailor both sensitivity and stability of the piezo-resistive responses, so that it was possible to monitor the strain evolution in the elastic domain and damage accumulation over this limit. Polymer matrices were selected after calculation of their χ Flory-Huggins parameters to evaluate their interactions with the PET substrate and solvent of dispersion, and after the comparison of their stress/strain characteristics, particularly their elastic limit. PC-1%CNT was found to be the best candidate satisfying both chemical and physical criteria. Finally, the exponential evolution of the piezo-resistive response of CPC sensing skins on a wide range of deformation (until breakage at ε = 27%), was well fitted with a model based on quantum tunnelling conduction inducing an exponential evolution of resistance with variations of CNT/CNT junction gap from 0.5 to 0.625 nm.