"It was low-key, on a boat," a source close to the couple tells PEOPLE. "It was a simple ceremony, exchanging vows."
According to a press release issued by TrimSpa, the diet-product company for which Smith is spokesperson, the couple, accompanied by a few friends and family and Smith's newborn daughter Dannielynn Hope, "made a commitment before God to be there for one another, to be each other's strength during this difficult time.
"Although the ceremony was officiated, it was not a wedding and no marriage certificate was issued."
On Tuesday Stern said on Larry King Live that he is the father of baby Dannielynn, born Sept. 7 – just three days before Smith's 20-year-old son, Daniel, died while visiting his mother in the hospital.
Stern told King of his relationship with Smith, "We love each other and it's been going on for a very long time and because of my relationship as her lawyer, we felt it was best to keep everything hidden. And we've done a pretty good job of that."
Wecht tells PEOPLE he reviewed tissue samples from Daniel on Thursday has now ruled out any natural cause of death. "There was nothing to suggest a subtle, cryptic, clinically asymptomatic condition, such as an inflammation of the heart," he said.
The death is still under investigation in the Bahamas.