Hello Ten! Yes, the animation of the character with the sword takes up 32x32 pixels. I'd say the best way to go is to consider the sword as a separate entity and put it on top of the character. The attack animation was based on the way it is done in "The Legend of Zelda: A Link to the Past", in that tileset the sword is a separate tile to be placed on top of the character (with a given offset).
The best would be to have the two as separate entities in the tileset. I can work on this quite quickly and update the file ;)