Is Legend of Zelda: The Wind Waker a sandbox game? In the general sense not really. The critical difference for me personally is the relative inability to experiment compared to the more traditionally-viewed sandbox games such as SimCity or Grand Theft Auto. While those two latter games allow players to not only trail off the intentioned play path, but also use the game mechanics to generate unexpected game moments The Legend of Zelda does not allow the same degree of freedom: you have the ability to explore but not to experiment in a sense.
That said, for my initial 30 minutes of play I set out to emphasize the adventure/exploration nature of The Wind Waker by purposefully avoiding completing the very first true objective given to the player: going back to their home to gather the necessary garments for Link (and eventually a weapon). Instead, I attempted to romp around Outset Island to explore what I could do without any of these items. In one interpretation I was very much attempting to roleplay as Link before his quest in The Wind Waker.
Outset Island and its inhabitants exist less as people and more as a tutorial for novice players to learn the particular game-isms of The Legend of Zelda series. It's actually interesting to note the various ways the landscape of the island, the NPCs living there, and even the small sidetasks are all explicitly designed to acclimate players to the basic controller functions that will be necessary to play the rest of the game. The simplest concepts: the necessity to collect rupees to buy things (reinforced in multiple ways), the basic combat system, and even the item collection/buying/button assignment mechanics are all explained at this juncture.
That said beyond these things there's very little to do on the island. In fact it's hard to merely kill oneself through accident, none of the falls initially present are large enough to hurt Link and the only way to lose health is by drowning in the ocean which only takes away a bare quarter of a heart.