We investigate the potentialities offered by the study of J/ψ exclusive photo-production in ultra-peripheral collisions at a fixed-target experiment using the proton and lead LHC beams (generically denoted as AFTER@LHC) on hydrogen targets and at RHIC in the collider mode. We compare the expected cross sections in both set-ups. Studying Single-Transverse-Spin Asymmetries (AN) in such a process provides a direct path to the proton Generalised Parton Distribution (GPD) Eg(x,ξ,t). We evaluate the expected precision on AN for realistic conditions with the LHCb detector in pH↑ and PbH↑ collisions. We also discuss prospects with polarised deuterium and helium targets in the case of AFTER@LHC.