Use an unregistered revolver. The bullet can't be traced, and you won't lose the casing because they don't discharge. After the body hits the ground, if you feel like it, kick the groin.
I saw a movie where the bullet was made of ice and the casing was disposed of.
That's why it's a movie: it doesn't work in real life. The "bullet" would be vaporized instantly
There's clips on YouTube where they use ice in place of shotgun shells. Horribly inaccurate but they do hold together