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Ya, if he went to a store wearing sunglasses and a trench coat, bought one of those throw away, one time use cell phones, wore gloves while handling the phone, used the bow tie voice changer to disguise his voice, call the boss, then throw the phone into the river, he could be pretty successful.
The glasses and trench coat (and hat) would be so surveillance cameras didn't capture him buying the phone, using a cheap over the counter one time use phone would be so the Organization would not trace the number, the gloves would make sure no finger prints were left on the phone, and then obviously the bow tie voice changer would be so that his voice couldn't be recognized, then throwing the phone into the river so no major evidence was left.
Or, to make it easier, we use Vermouth's phone and the bow tie voice changer to call up the boss. I'm sure with a little persuasion (maybe even a couple of judo throws)Vermouth would give in.