Visit any bar that takes their cocktails seriously, and they’re probably serving Manhattans and Martinis in small, rounded coupe glasses instead of the usual triangular cocktail glasses. I recently made the switch at home and I support it.
One could argue that vintage glassware is just another hipster affectation (the twirled, wax mustache of the cocktail renaissance), but I like the nod to the golden age of mixology.
So anywhere I mention “coupe glass”, feel free to use the triangular cocktail glasses you already have. But I don’t think you’d regret the minimal investment required for a more elegant vessel.