From the glasses with the conical shape you usually drink martini or cocktails. "Shaken, not stirred!" is how James Bond mostly enjoys his favorite drink.
The cocktail glass emoji was introduced in 2010 and released as part of the Unicode 11.0 standard. This emoji can be found under the food and drink
category. Because the cocktail glass emoji has been around for quite some time, it should display correctly in the majority of operating systems.