+25% damage
-34% clip size
-15% un-holster speed

Looks like an uncut stock shotgun, the look says "mid-distance" so maybe -20% spread and 20% slower un-holster?
One could also make it anti-FaN, decreasing the pellet amount but increasing damage per pellet.
So, something akin to Shortstop, but for Soldier/Engi/Pyro I guess.

Don't really want to touch the overall damage not to make it straight up a better shotgun for closer distances.

The original counterpart for this weapon was capable of slam fire, which allowed the gun to fire continuously without letting go of the trigger, only requiring holding down the trigger and rapidly pumping the shotgun to achieve slam fire. So to give it a similar effect I would go

+20% faster firing speed
+25% clip size
-15% damage penalty

honestly, it would be awesome as a reskin for stock

since it looks like the trench shotgun, ima try to make the stats be similar to it.

+10% damage to full health enemy
+25% damage to low health enemy
+30% faster firing speed
-25% slower reload speed
-10% slower move speed
-20% less accurate
-5% less damage

Press F to slam fire on a unsuspecting heavy

The Dug-Out Duster
Level 15 Modular shotgun

= Special key (Mouse 3 usually): attach or detach the following:
1. Knife Alt Fire: jab the gun foward, dealing Melee damage (equal to stock knife minus backstab)
2. Grenade Launcher Alt Fire: launches a single Stock pipe bomb at enemies, reload after every shot, consumes 6 shotgun ammo per pipe
3. Flashlight Alt Fire: Turn on the flashlight to reduce shotgun spread (don't ask how it's Soldier/Mann.Co Logic)
4. None/Default: 20% faster weapon switch-to speed and 15% faster weapon switch-from speed.
- 30% slower Switch-to Speed
- No Random Crits