It is possible but hard it took me along time to get to ganon i had to use the sword but my prefered weapon was bow and arrow . I just didnt like the fact that it took my hard earned my rupees .
If you are talking about the original Legend of Zelda, you are able to go swordless until you reach Gannon because you need a sword to kill him. (It was spelled Gannon in the original Legend of Zelda by the way)