The near-Earth asteroid (1917) Cuyo was subject to radar and light curve observations during a close approach in 1989, and observed up until 2008. It was selected as one of our ESO Large Programme targets, aimed at observational detections of the Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect through long-term light curve monitoring and physical modelling of near-Earth asteroids. We aim to constrain the physical properties of Cuyo: shape, spin-state, and spectroscopic & thermophysical properties of the surface. We acquired photometric light curves of Cuyo spanning the period between 2010 and 2013, which we combined with published light curves from 1989-2008. Our thermal-infrared observations were obtained in 2011. Rotationally resolved optical spectroscopy data were acquired in 2011 and combined with all available published spectra to investigate any surface material variegation. We developed a convex light-curve-inversion shape of Cuyo that suggests the presence of an equatorial ridge, typical for an evolved system close to shedding mass due to fast rotation. We determine limits of YORP strength through light-curve-based spin-state modelling, including both negative and positive acceleration values, between -0.7x10^-8^rad/day^2^ and 1.7x10^-8^rad/day^2^. Thermo-physical modelling with the ATPM provides constraints on the geometric albedo, pV=0.24+/-0.07, the effective diameter Deff=3.15+/-0.08km, the thermal inertia =44+/-9J/m^2^/s^1/2^/K, and a roughness fraction of 0.52+/-0.26. This enabled a YORP strength prediction of (-6.39+/-0.96)x10^-10^rad/day^2^. We also see evidence of surface compositional variation. The low value of YORP predicted by means of thermophysical analysis, consistent with the results of the light curve study, might be due to the self-limiting properties of rotational YORP, possibly involving movement of sub-surface and surface material. This may also be consistent with the surface compositional variation that we see. The physical model of Cuyo can be used to investigate cohesive forces as a way to explain why some targets survive rotation rates faster than the fission limit.