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Recent years have seen a growing sample of TeV emission detections in gamma-ray burst afterglows, as well as an increasing role for structured jets in afterglow modelling. Using a kinetic approach, we show that the structure of an afterglow jet impacts its TeV emission, with jets where the energy falls off more sharply with angle showing a decrease in Inverse Compton (IC) peak flux relative to synchrotron peak flux. We use a modified version of the code katu, to which we have added adiabatic expansion and a fully self-consistent treatment of IC cooling both for the electron and photon populations. We compare our results to the semi-analytical code afterglowpy, finding a good agreement with our model except at early times off axis where the effects of baryon loading are important. We compare electron cooling in the cases where there is no IC cooling, Thomson cooling and an inclusion of Klein-Nishina effects, finding that the spectra can only be distinguished if the Compton potential is significantly increased. The smooth and gradual transition of our KN cooling also leads to a disparity in the cooling between our results and semi-analytical solutions based on asymptotic limits. Finally, we combine best fit parameters from afterglowpy to reproduce the light curves of GRB 170817A in our model. For our choice of parameters, we find that GRB 170817 would not have been detected in the TeV domain if seen on-axis, even by the upcoming Cherenkov Telescope Array Observatory., Comment: 20 pages, 13 figures.This is a pre-copyedited, author-produced PDF of an article accepted for publication in Monthly Notices of the Royal Astronomical Society following peer review