Sniff sniff

This in fact is not a spoken word so much as a sound. It is the same sound made when someone is sniffing their nose as they are crying or trying to stop crying. The recovery sniffs is the sound you are mocking. It is a sarcastic way to show someone you feel no pity for their situation. Just like playing the tiny violin for a person, this mocks the persons sadness by "crying" along with them. See example