It might be advisable to skip the Cobalt Sword because of its lackluster stats compared to Phasesabers and the pre-HardmodeNight's Edge. Compared to Phasesabers, the Cobalt Sword only has slightly higher knockback, while the only disadvantages the Night's Edge has are its complicated crafting as well as (outside of the Desktop version) its slow use and lack of inherent autoswing.
The Cobalt Sword bears a strong resemblance to the Muramasa and the Japanese Katana, and fits with the "Feudal Asia" theme of other Cobalt weapons and armor.
The Cobalt Sword has the fastest speed of all Hardmode Ore swords. This may be because it resembles the real-world Katana, a very light, thin blade (which is also in Terraria).