Ship tracks, bright lines in clouds formed by ship exhaust, serve as "natural laboratories" for investigating aerosol-cloud interactions, one of the largest sources of uncertainty in the human forcing of the climate. Observing ship tracks has been used to help constrain the effect of anthropogenic aerosols on cloud brightness, amount and water content. The validity of these constraints relies, in part, on the accuracy of satellite retrieval algorithms used to measure cloud properties. A known source of uncertainty in these algorithms is the representation of the droplet size distribution. Standard bi-spectral retrievals (e.g. MODIS) rely on a fixed effective variance (v_eff) for the modified gamma distribution used to model cloud droplet dispersion. The introduction of aerosols into clean, marine clouds produces not only smaller droplets but also a narrower size distribution, contradicting this fixed assumption. This study utilises a synthetic retrieval experiment to quantify the impact of this assumption on cloud property retrievals and the derived aerosol-cloud interaction metrics. The results produced indicate that neglecting the narrowing of the droplet size distribution causes a systemic overestimation of effective radius (r_e) of approximately 3% in the polluted regime, while optical depth (τ) is virtually unaffected. Consequently, liquid water path (LWP) is robustly retrieved with a small bias of under 3%, which is expected due to the linear dependence of LWP on r_e and τ. Cloud droplet number concentration (N_d), however, suffers from a much larger overestimation of approximately 24% in freshly polluted clouds. This discrepancy is driven by the inverse dependence of N_d on the spectral width parameter k, inflating the droplet count as the true distribution narrows. This inflation of droplet number in ship tracks may exaggerate the apparent susceptibility of clouds to aerosols, potentially overstating the Twomey effect in observation-based estimates reliant on data from ship tracks. This may also lead to an overestimation the efficacy of climate intervention efforts, such as marine cloud brightening, if monitored by satellite.