Compact, star-forming galaxies with high star formation rate surface densities (ΣSFR) are often efficient Lyman continuum (LyC) emitters at z ≤ 4.5, likely because intense stellar feedback creates low-density channels that allow photons to escape. Irregular or disturbed morphologies, such as those resulting from mergers, can also facilitate LyC escape by creating anisotropic gas distributions. We investigated the influence of galaxy morphology on LyC production and escape at redshifts 5 ≤ z ≤ 7 using observations from various James Webb Space Telescope (JWST) surveys. Our sample consists of 436 sources, which are predominantly low-mass (∼108.15 M⊙), star-forming galaxies with ionizing photon efficiency (ξion) values consistent with canonical expectations. Since direct measurements of fesc are not possible during the Epoch of Reionization (EoR), we predicted fesc for high-redshift galaxies by applying survival analysis to a subsample of LyC emitters from the Low-Redshift Lyman Continuum Survey (LzLCS), selected to be direct analogs of reionization-era galaxies. We find that these galaxies exhibit, on average, modest predicted escape fractions (∼0.04). In addition, we evaluated the correlation between morphological features and LyC emission. Our findings indicate that neither ξion nor the predicted fesc values show a significant correlation with the presence of merger signatures. This suggests that in low-mass galaxies at z ≥ 5, strong morphological disturbances are not the primary mechanism driving LyC emission and leakage. Instead, compactness and star formation activity likely play a more pivotal role in regulating LyC escape.