The interdisciplinary nature of Child-Robot Interaction (CRI) fosters incorporating measures and methodologies from many established domains. However, when employing CRI approaches to sensitive avenues of health and wellbeing, caution is critical in adapting metrics to retain their safety standards and ensure accurate utilisation. In this work, we conducted a secondary analysis to previous empirical work, investigating the reliability and construct validity of established psychological questionnaires such as the Short Moods and Feelings Questionnaire (SMFQ) and three subscales (generalised anxiety, panic and low mood) of the Revised Child Anxiety and Depression Scale (RCADS) within a CRI setting for the assessment of mental wellbeing. Through confirmatory principal component analysis, we have observed that these measures are reliable and valid in the context of CRI. Furthermore, our analysis revealed that scales communicated by a robot demonstrated a better fit than when self-reported, underscoring the efficiency and effectiveness of robot-mediated psychological assessments in these settings. Nevertheless, we have also observed variations in item contributions to the main factor, suggesting potential areas of examination and revision (e.g., relating to physiological changes, inactivity and cognitive demands) when used in CRI. Findings from this work highlight the importance of verifying the reliability and validity of standardised metrics and assessment tools when employed in CRI settings, thus, aiming to avoid any misinterpretations and misrepresentations.