As the vision of global-scale unconditional information security becomes gradually realized, the importance of inter-satellite quantum communications has been rapidly increasing. The recently proposed round-robin differential-phase-shift (RRDPS) quantum key distribution (QKD) protocol has attracted much attention not only due to its potential high error tolerance, but also due to its distinct feature that the information leakage can be bounded without monitoring signal disturbances. Despite many existing implementations over fiber-optic channels, the feasibility of RRDPS QKD over an inter-satellite channel is still unknown. Moreover, despite the current advances in orbital angular momentum (OAM) encoding and temporal mode (TM) encoding, most of the existing studies on RRDPS QKD are restricted to time-bin encoding. In this work, we remedy this situation by exploring the feasibility of performing RRDPS QKD using OAM encoding and TM encoding over an inter-satellite channel. Our results indicate that OAM encoding is preferable to time-bin encoding only under the circumstances where a low dimension and a large receiver aperture are used. However, we find that TM encoding is the best encoding scheme in RRDPS QKD over an inter-satellite channel. In particular, we show that TM encoding not only leads to the best performance and the largest feasible parameter range, but also, for the first time, enables all the theoretically available advantages of an increased dimension to be realized in the context of RRDPS QKD.