Its not a hawaiian instrument, nor a mixed drink, nor even a shananagan of any sort. This word is a word used when drunk and exiting a casino in Las Vegas. Usually followed by several magic tricks preformed by a very large man and a very silent man, usually close to the end of the calendar year.
When asked to give an example of "shalele", the kind sir had a perplexed look on his face, as if he had just been asked to solve a quadratic equation or discover the origins of goat cheese. Then he exclaimed, "Hand me that shalele over there and we'll figure it out, mate!"