Sotto voce means to lower the sound of your voice, not out of embarrassment or fear but more for emphasis. it’s a dramatic technique and also used in music and screenplay writing. I especially liked the Wiki reference to Galileo Galilei’s sotto voce utterance “Eppur si muove (And yet [the Earth] moves’.
Some more quotes from literature:
“I still can’t believe,” Michael said, sotto voce, “that you came to the Vampires’ Masquerade Ball dressed as a vampire.”
― Jim Butcher, Grave Peril
“Is it life-threatening?” they asked. They said it slightly sotto voce, but you could hear the thirst for sensation right through it: when people get a chance to come close to death without having it touch them personally, they never miss the opportunity.”
― Herman Koch, The Dinner