Low-Earth orbit (LEO) non-terrestrial networks (NTNs) have become increasingly popular due to their ability to provide high-bandwidth communication in otherwise unserved regions. However, this comes at the cost of high satellite mobility, necessitating efficient handover (HO) strategies. Till now the focus has been on the S-band, however Ka-band is expected to be deployed for high-bandwidth applications necessitating HO studies for higher frequency bands. To address this, we evaluate the performance of the conventional received power-based HO, as well as alternatives such as elevation angle and distance-based triggers for Ka-band LEO networks, and compare them with S-band frequencies. Moreover, a dynamic threshold approach is also evaluated in terms of the number of HOs, unnecessary handovers (UHOs), radio link failures (RLFs), and distributions of downlink carrier-to-noise-plus-interference ratio (CNIR) and mean time-of-stay of a user in a cell. The obtained results indicate the efficacy of power-based mechanisms for the S-band while showing that the alternative methods provide a much better balance at the Ka-band in terms of the overhead and the overall communication link quality.