This one really isint a weapon, more like equipment.

The Sheikah Garb

This slightly tight fitting stealth suit with all the bells and whistles of traditional Sheikah armour (bandage type things like on Sheik, metal, and the obligatory Sheikah symbol) allows link to run faster, dodge quicker and better, and even become "invisible" to enemies ( a la stone mask) when in shadow. Also, it allows Link to jump with a button command! It also provides him with assorted weaponless attacks. All of these awesome features come at the cost of some defensive power and maybe the loss of using a shield.

This suit would not be mandatory to the quest. It would be obtained by talking to Link's father, a former Sheikah archer for the Royal Family, and playing through mini missions as him through "stories." After completing 10 or so missions he would say that he is glad that Link seems more interested in his Sheikah heritage than his Hylian roots (promoted through his Uncle's sword lessons) and give him this suit.