I would propose at the beginning of the trip as opposed to the end of the trip (it would take some of the stress off yourself and your future bride's vacation will be all that more enjoyable). I should also point out that the sunsets in Aruba are spectacular, hence you may want to consider proposing in the early evening. Perhaps you look into the Hyatt's sunset service (from their website):
Sunset Service
There's no better way to start your evening than reclining in teak Adirondack chairs overlooking the beach, nibbling on gourmet hors d'oeuvres and sipping a glass of your favorite wine. Consider this your own private happy hour, complete with a tuxedo-clad waiter to take care of every detail. Select your menu from an enticing selection of hot and cold hors d’oeuvres, wines, champagnes, chocolate dipped strawberries, or even a Monte Cristo #2 Cigar.
Sunset Service is located on the beach in front of the Palms restaurant. Proper attire: Black Tie to Black Bikini, whichever you prefer!
Click here to view our Sunset Service Menu.
Perhaps you could arrange to have your waiter bring the ring over with the hors d'oeuvres/champagne at sunset.