Melee Quick-Draw Sheath seem to hold any(?) type of melee weapons and provide a bonus Minor Action when used, but it doesn't seem as if it on its own allow you to take the actual quick draw action. Unless perhaps the melee weapon happen to be pistol sized or otherwise allowed to be quick drawn by default anyway.
Having said that, the Weapon Flash 2-edge action let you to take the Quick Draw Minor Action for any melee weapon (and if used together with a Melee Quick-Draw sheath you would even get the Minor Action back). And the Martial Art Technique Iaijutsu let you do something similar as long as you limit yourself to weapons small enough to be wielded in one hand.
Quick-Draw Scabbard, on the other hand, allow any melee weapon to be quick drawn in itself (where each scabbard is for a specific melee weapon), but then again, unlike the Quick-Draw Sheath - it doesn't provide any bonus minor action.
