Syrup:

In small saucepan, bring the water and sugar to a boil over medium high-heat. Simmer until the sugar has dissolved completely. Set aside to cool.

Put the chile-lime powder on a small plate. Using the lime wedge, moisten the rims of the martini glasses. Invert the martini glasses into the chile-lime powder, to coat the rims.

In a blender, combine the simple syrup, cucumber, water, and lime juice until smooth. Strain the mixture into a pitcher. Add the vodka and mix well. Fill a martini shaker with ice and add about 1 cup of the prepared cucumber mixture. Shake well and serve.