Shake lime mezcal, ginger juice, lime juice, prickly pear purée, and egg white in a cocktail shaker (or in a tightly lidded 1-qt. glass jar) until frothy, about 1 minute.
Fill shaker with ice, cover, and shake again until outside is frosty, about 30 seconds.
Strain through a fine-mesh sieve into a glass.
Garnish with a few edible flowers.