There actually is a precedent for a private swearing-in ceremony. (Not that I'm advocating it, just saying that it's happened before.)

President Calvin Coolidge was sworn into office by his father, in his own home in the middle of the night. It's in his autobiography. He did not lay his hand on the Bible to swear the oath, but there was one on the table.

"The oath was taken in what we always called the sitting room, by the light of the kerosene lamp, which was the most modern form of lighting that had then reached the neighborhood. The Bible which had belonged to my mother lay on the table at my hand. It was not officially used, as it is not the practice in Vermont or Massachusetts to use a Bible in connection with the administration of an oath.

Besides my father and myself, there were present my wife, Senator Dale, who happened to be stopping a few miles away, my stenographer, and my chauffeur."

[link to www.eyewitnesstohistory.com]