Archers would go for melee attack in options where either we have to be in the mobs face or if there is a certain amount of delay between shots etc. In a dungeon you might be locked into to close quarter areas like small hallways and what not. I would go with option 1 of the OP because it makes the most sense and an Archer would never attack with his bare fists for obvious reasons. His hands are really important and wouldn't take a chance in breaking a finger when having to pull bowstrings. Even if you just gave us a simplified dagger for looks like a hunting knife instead of having using your fists I would be happy.
Actually a lot of bows in the old days could be used as a weapon themselves close range because they were very sturdy and strong made of special wood that won't break from pressure. You could always make it where an Archer slaps the enemy with the bow and the animations would be fairly simple to design.
