a handgun on a stick is a carbine rifle.
ie: a short barrelled rifle.
The classic examples would be the german schmeisser - a machine pistol with a fold out stock. And the mauser where the wooden holster, can be attached to the gunn butt to make a longer stock and lets the gun be fired almost like a carbine.
https://www.afg-defense.eu/replica-pistol-mauser-c-96-nemecko-wood/As a general rule that kind of thing makes a pistol more accurate.
This is because your brain has a much longer straight line to sight along and extrapolate the bullet's path with.
And the pistol can be held a lot steadier.
Though what you are suggesting is probably to hold it one handed.
Where the weight is the main factor, so you can't really draw any correlation to how a sling works.