Icicle would be a bad choice. With any bladed or pick type melee weapon, there's going to be blood spatter. You may get rid of the murder weapon but there's still ways to tie the crime to you. Especially if it gets on your clothes or shoes. You could burn them, but you'd have to make sure you weren't seen doing so, or even wearing or carrying the bloody items.
I'd personally go with poison. A fast acting one that metabolizes quickly. Difficult to detect during the toxicology screenings. It's also more discrete and leaves little evidence provided you don't obtain it through legal channels.