Photoswitchable self-assembled monolayers (SAMs) in contact with a conductive or semiconductive layer can be used to remotely trigger changes in electrical current using light. In this study, we apply full-atomistic simulations to assess the changes in electronic structure and charge-transport properties of a graphene sheet in contact with an amorphous silica dielectric decorated by an azobenzene SAM. The simulations explicitly account for the structural and electrostatic disorder sourced by the dielectric, which turns out to be weakly affected by photoisomerization and spatially correlated over a length scale of 4-5 nm. Most interestingly, by combining large-scale (tight binding) density functional theory with Kubo-Greenwood quantum transport calculations, we predict that the trans-cis isomerization should induce a shift in surface electrostatic potential by a few tenths of a volt, accompanied by a variation in conductivity by a factor of about 3.