I posit this question to you:
What's the difference between Firebug and Demolitions in their "niche"?
Firebug has light, penetrating area-effect, constant streams of damage that continues over time with very little damage to himself. Good at close range, poor in open areas, inexpensive, and excels in corridors (You'll hit every unit in the area as the stream penetrates).
Demo man does instant heavy, area-effect damage with high reload times and a big possibility of hurting yourself. Suicide at close range, poor in corridors (You'll only hit units in front and are likely to hurt yourself), good in open areas, and very expensive.
Very different, though Demoman is generally more powerful because he has more weapon choices at the moment. Plus, all of those classes have unique weaponry.
Meanwhile, Gunslinger would basically steal away 2 Sharpshooter weapons and add a third one. While I'm in favor of a Sharpshooter nerf, taking a classes core weapons to create another class that's not really needed is a bad idea.
Seriously, though, what is it's niche? The zed-time thing would be gimmicky at best and annoying to teammates at worst. (Don't pretend that zerkers/Commandos chaining 5 Zed-Times together when you're just trying to run somewhere or reload hasn't been annoying!).
There's no way it could do area-effect better than Demo/Firebug/Support, so the role would need to be something else. Sweeping would be it's only viable role (Seeing as how it steals the Sharpshooter's sweeping 9mm and Handcannons) and it'd still struggle to meet the SCAR Commando or M14 Sharpshooter at that.
So the only really open option left is to make it a single-target High-DPS. The Handcannons kinda do that, but they really need the Sharpshooter's headshot bonuses to shine, so you'd be stuck adding a high-damage low-rate-of-fire weapon: The revolver.
Thus, for all intents and purposes, you have a Sharpshooter class with no headshot bonuses and a Revolver replacing the M14/Crossbow. I'm sorry, but it's a bad idea. Cool concept, but it just doesn't fit. You can try to argue it all you want, but that's what it really comes down to.