The Sondheimer dialkyne reagent has previously been employed in strain-promoted double-click cycloadditions with bis-azide peptides to generate stapled peptide inhibitors of protein–protein interactions. The substituted variants of the Sondheimer dialkyne can be used to generate functionalized stapled peptide inhibitors with improved biological properties; however, this remains a relatively underdeveloped field. Herein, we report the synthesis of new substituted variants of Sondheimer dialkyne and their application in the stapling of p53-based diazido peptides to generate potent stapled peptide-based inhibitors of the oncogenic p53-MDM2 interaction. The functionalized stapled peptide formed from a meta-fluoro-substituted Sondheimer dialkyne was found to be the most potent inhibitor. Furthermore, through experimental studies and density functional theory calculations, we investigated the impact of the substituent on the strain-promoted double-click reactivity of Sondheimer dialkyne.