Assassin's Knife

The Assassin's Knife is a Pre-Hardmode melee weapon dropped from any underground enemy (1/1000)

It has very little range. Yet, it can be swung insanely fast with Auto-Swing. This creates a relatively high DPS in close quarters combat.

(Note: the Auto-Swing abilities of this weapon are similar to the Arkhalis', where if you are holding down left click, the knife will create a chainsaw-like, rapid stab. This is because of the insanely low use time.)