1) Replace the invocation with a nice thank-you speech to the People for their participation in this peaceful transition of power. They are the ones who make it possible. Follow that with a moment of respectful silence. Those in attendance may encode and transmit thought waves* to The Noodly One (or other deity of choice) during that moment, or not, as preferred.
2) Swear in with one hand on a copy of the US Constitution, since that's the document I'm swearing to defend and uphold.
3) Say "This I vow" or something similar at the end of the swear-in.
4) Yo-Yo Ma? Sweet! Let's hear more John Williams arrangements! (We'd all rather hear that than my speech, wouldn't we?)
* Thought waves, by definition, must be analog. Right? When's the transition to digital scheduled to occur?