Vibrational Strong Coupling (VSC) has been reported to change the rate of organic reactions. However, a lack of convenient and reliable methods to measure reaction kinetics under VSC makes it challenging to obtain mechanistic insight into its influence, hindering progress in the field. Here, we use recently developed fixed-width optical cavities to obtain large kinetic datasets under VSC with small errors (± 1-5%) in an operationally simple manner using UV-vis spectroscopy. The setup is used to test whether VSC changes a fundamental kinetic property of polar reactions, nucleophilicity, for water and alcohols, species commonly used in VSC-modified chemistry. We determined the rate constants for nucleophilic capture with a library of benzhydrilium ions as reference electrophiles with and without strong coupling of the nucleophile's key vibrations. For all investigated combinations of electrophiles and nucleophiles, only minor changes in the observed rate constants of the reactions were observed, independently of the coupled bands. These results indicate that VSC does not substantially alter the nucleophilicity of water and alcohols, suggesting that polar reactions are modified through other, presently unknown mechanisms. Fixed-width cavities allow for convenient and reproducible UV-vis kinetics, facilitating mechanistic studies of VSC-modified chemistry.