The classification of galaxy mergers and isolated disks is key for understanding the relative importance of galaxy interactions and secular evolution during the assembly of galaxies. The kinematic properties of galaxies as traced by emission lines have been used to suggest the existence of a significant population of high-z star-forming galaxies consistent with isolated rotating disks. However, recent studies have cautioned that post-coalescence mergers may also display disk-like kinematics. To further investigate the robustness of merger/disk classifications based on kinematic properties, we carry out a systematic classification of 24 local (U)LIRGs spanning a range of galaxy morphologies: from isolated spiral galaxies, ongoing interacting systems, to fully merged remnants. We artificially redshift the WiFeS observations of these local (U)LIRGs to z=1.5 to make a realistic comparison with observations at high-z, and also to ensure that all galaxies have the same spatial sampling of ~900 pc. Using both kinemetry-based and visual classifications, we find that the reliability of kinematic classification shows a strong trend with the interaction stage of galaxies. Mergers with two nuclei and tidal tails have the most distinct kinematic properties compared to isolated disks, whereas a significant population of the interacting disks and merger remnants are indistinguishable from isolated disks. The high fraction of late-stage mergers showing disk-like kinematics reflects the complexity of the dynamics during galaxy interactions. However, the exact fractions of misidentified disks and mergers depend on the definition of kinematic asymmetries and the classification threshold when using kinemetry-based classifications. Our results suggest that additional indicators such as morphologies traced by stars or molecular gas are required to further constrain the merger/disk classifications at high-z. ; Comment: 16 pages, 5 figures, ApJ accepted