Hideous Laughter is a 1st level spell with a comparable effect to the Taser-Pistol's special ability.
Justification: It is a ranged spell, requiring a failed saving throw leaving the target incapacitated and prone. (For anyone targeting the creature in melee, this is similar to attacking a stunned creature; although the prone makes hideous laughter less useful for a ranged attacker.) Hideous laughter has an advantage of having a potentially longer duration if subsequent saving throws are failed; unlike the Taser-Pistol it doesn't require the player to also hit first. It also has the disadvantage of being ineffective against low Intelligence creatures.
The Taser-Pistol ability has a large advantage of being one effect of an attack of a light weapon; and so potentially just one of many things that can happen on an attack action.
If you accept this premise, then it is useful to look at other magic items which allow you to cast 1st level spells:
Eyes of Charming: Uncommon; 3 charges of Charm Person per day.
Ring of Obscuring: Uncommon; 1d3 charges of Fog Cloud per day.
Wand of Entangle: Uncommon; 1d6 + 1 Entangles per day.
Wand of Magic Detection: Uncommon; 1d3 charges of Detect Magic per day.
Wand of Magic Missiles: Uncommon; 1d6 + 1 charges of Magic Missile per day.
Staff of Healing: Rare; among other options, you could use this to cast 1d6+4 Cure Wounds a day.
Staff of Charming: Rare; among other bonuses, you could use this to cast 1d8+2 first level spells (Charm Person, Command or Comprehend Languages) per day.
The main distinction between the Uncommon and Rare magic items which can cast 1st level spells, is that the Rare items are a little more versatile. They all do something a little bit more than just casting the spell. I would argue that also being a functional weapon easily pushes the Taser-Pistol into the Rare category.
The other major difference between the Taser-Pistol and most magic items is that the effect has a recharge which doesn't require a rest. It is realistic to expect this to proc once or twice per combat, but for "boss fights" - potentially a lot more. If your DM is following the DMG guidance of 6-8 medium to hard encounters per day, that's more uses per day than most magic items have. If it were say "recharges during a short rest", I would call it a Rare item. As it stands the fact that this item has a large potential impact I would label it as Very Rare.