An analytical and numerical investigation is undertaken to study the effects of non- standard orbit topology on stochastic ripple diffusion of high-energy ions in tokamaks. Finite orbit-width effects are demonstrated to lead to large modifications of the threshold for the onset of stochastic motion. Trapped particles moving along trajectories with turning points on the inside of the torus are most severely affected. In particular, orbits close to the pinch orbit are very sensitive to magnetic field ripple, whereas orbits with bounce points close to the horizontal midplane are less easily perturbed than suggested by small orbit-width theory. Applying the results to recent ripple experiments on JET, we find that the number of stochastically moving particles is only moderately affected by these effects. The reason for this is the large ripple amplitude and the steepness of ripple gradient over most of the plasma cross section.