Black holes in dwarf/bulgeless galaxies play a crucial role in studying the co-evolution of galaxies and their central black holes. Identifying massive black holes in dwarf galaxies suggests that the growth of black holes could precede that of galaxies. However, some of the most intriguing candidate active galactic nuclei (AGN) in small galaxies have such low luminosities that the sample is vulnerable to contamination by other sources, such as supernova remnants. We re-analysed Chandra X-ray Observatory observations of candidate AGN in Henize 2-10 and NGC 4178, considering the potential signals of emission lines in the minimally-binned X-ray spectra. We find that hot plasma models, which are typical of supernova remnants, explain the observed spectra much better than simple power-law models, which are appropriate for AGN. We identify clear signals of X-ray lines in the faint X-ray source identified with the radio source in Henize 2-10 by Reines et al. 2016. Combining our work with the MUSE measurement of the ionization parameter in this region by Cresci et al. 2017 indicates that this radio and X-ray source is more likely a supernova remnant than an AGN. A similar analysis of the low-count X-ray spectrum of a candidate AGN in NGC 4178 shows that a hot plasma model is about seventeen times more probable than a simple power-law model. Our results indicate that investigation of X-ray spectra, even in a low-count regime, can be a crucial tool to identify thermally-dominated supernova remnants among AGN candidates.