Context. Tidal interactions of galaxies in galaxy clusters have been proposed as one potential explanation of the morphology-density relation at low masses. Earlier studies have shown that galaxy harassment is a suitable mechanism for inducing a morphological transformation from low-mass late-type disk galaxies to the abundant early-type galaxies. Aims. The efficiency of tidal transformation is expected to depend strongly on the orbit of a galaxy within the cluster halo. The orbit determines both the strength of the cluster's global tidal field and the probability of encounters with other cluster members. Here we aim to explore these dependencies. Methods. We use a combination of N-body simulation and Monte-Carlo method to study the efficiency of the transformation of late-type galaxies by tidal interactions on different orbits in a galaxy cluster. Additionally, we investigate the effect of an inclination between the disk of the infalling galaxy and its orbital plane. We compare our results to observational data to assess the possible relevance of such transformations for the existing cluster galaxy population. Results. We find that galaxies that entered a cluster from the outskirts are unlikely to be significantly transformed (stellar mass loss ≤6%). Closer to the cluster centre, tidal interactions are a more efficient mechanism (stellar mass loss up to 50%) for producing harassed galaxies. The inclination of the disk can reduce the mass loss significantly, yet it amplifies the thickening of the galaxy disk. Galaxies with smaller sizes on intermediate orbits are nearly unaffected by tidal interactions. The tidal influence on an infalling galaxy and the likelihood that it leads to galaxy harassment make a very stochastical process that depends on the galaxy's specific history. Conclusions. We conclude that harassment is a suitable mechanism that could explain the transformation of at least a fraction of galaxies inside galaxy clusters. However, the transformation would have to start at an early epoch in protocluster environments and continue until today, in order to result in a complete morphological transformation.