I love cucumber just by itself. It is an unusual breakfast choice, but there's nothing wrong with it- although cucumber wouldn't be very filling and I suppose you'd get hungry by mid-morning.
One of Anna Thomas' Vegetarian Epicure books has a recipe for cucumbers which she describes as trying to become dill pickles and not quite making it... but I don't know that half-dill-pickles would suit you for breakfast...
Let me know if you want me to post the recipe.
I think you could buy a water distiller for home use.
Every snowflake in an avalanche pleads, "Not guilty". Stanislaw J. Lec