Are there guns that are designed to collect spent cases?
I have some business to take care of and can’t afford evidence falling somewhere where I can’t find it…
Brass catcher. Or use a revolver.
Do you have a friend to help you with the body?
Caseless ammunition.
Some Italian machine guns put the empties back into the feed strips (mostly for vehicle use where you don’t want them spilling out onto the floor)
The easiest way is to use any brand or model of revolver…
Better yet, use a crossbow. No GSR !
With a bolt made of ice. No evidence at all.
Or a double-barrel shotgun in case you aren’t a good shot.
Dry ice. An ice arrow will leave water behind, which is evidence. Dry ice just sublimates away. 
What are you going to do? Whack somebody? Don’t you realize law enforcement people read these threads?
Like everyone else said use a revolver and empty the shells in an undisclosed location.
Using an icicle to exit someone would be a good way to go. Even though they could probably tell in an autopsy that an icicle was used, the weapon is gone and evaporated in short order.
Not that I have thought much about this, mind you.
Handgun: revolver - the cartridge cases are left in the cylinder.
Shotgun: double-barrel or over-under - the shells are not ejected until you open the action.
Rifle: single-shot - the shells are not ejected until you open the action.
Muzzleloader: no shell casings to worry about.
Mythbusters couldn’t get an ice bullet to work. When fired they never made it past the muzzle. If they did make it out of the bullet mold.
Since you are leaving the bullets, what’s the problem with the cases? Just be sure to wear gloves when handling them.
Don’t worry about the shell casings. The trick is to use a gun that can’t be linked to you and be sure to just leave it at the scene. Modern forensics isn’t anywhere near as miraculous as television detective shows make it seem. They almost never get usable fingerprints from pistols or spent shell casings in real life. But if your victim is killed with 9mm ammunition, the piglets catch you with a 9mm pistol, and the state can prove you had motive, the jury is probably going to convict your ass whether the bullets can be directly linked to the gun or not.
Come on guys, The Godfather is more than 40 years old, you should know this stuff.