\textit{Metric Differential Privacy} enables text-to-text privatization by adding calibrated noise to the vector of a word derived from an embedding space and projecting this noisy vector back to a discrete vocabulary using a nearest neighbor search. Since words are substituted without context, this mechanism is expected to fall short at finding substitutes for words with ambiguous meanings, such as \textit{'bank'}. To account for these ambiguous words, we leverage a sense embedding and incorporate a sense disambiguation step prior to noise injection. We encompass our modification to the privatization mechanism with an estimation of privacy and utility. For word sense disambiguation on the \textit{Words in Context} dataset, we demonstrate a substantial increase in classification accuracy by $6.05\%$.