You need BOTH! A lightweight tote with a zipper is needed for excursions and something smaller (removeable over the shoulder strap/clutch) for on-board strolls, meals, shows, etc.
My favorite totes to take on a cruise has always been Vera Bradley because they're lightweight, have zippers, comfortable shoulder straps, and a multitude of pockets.
Have fun! Hope you love cruising as much as I always did!!