wouldn't that technically be drowning since the person is choking on water? Genius.
If you really wanted to get nutty with it, you could easily go all Dexter with it. Get them on the Dexter table, wrap them up, force their mouth open and shove the icicle down there until they die. Melt it and drink it, no evidence there. Hang the body upside down and drain all the blood from it, then take off the limbs, finger nails, teeth, hair, etc etc. Put everything into a barrel and use whatever they used on Breaking Bad to get rid of shit, can't remember off the top of my head. Before doing so, burn off your finger prints somehow and shave your entire body clean so there is no hair on it so none of that can be left at the scene. Get rid of your barrel of goodies and you're golden.