You can choose to either peel the cucumber or not. The peel will lend a stronger green hue to the slushie but also a subtle bitterness.
Elderflower syrup can be found in the ready-to-drink aisle of the supermarket. You can also use cane syrup or simple syrup (a syrup made from equal parts water and sugar).
When ready to serve, you can add a shot of alcohol, such as St-Germain or white rum.