Yeah, we still have the "so help me God" phrase in Oklahoma. I just went with it without saying anything (mostly because I'm shy), but later heard that you can ask for an affirmation and by law they have to allow that.
Speaking of which, does anyone know what the raising your right hand thing is about? Does it have religious significance or is it just some cultural thing?
Here's what Wikipedia has to say about the phrase in the States' court system:
"Some of the states have specified that the words "so help me God" were used in oath of office, and also required of jurors, witnesses in court, notaries public, and state employees. Where this is still the case, there is the possibility of a court challenge over eligibility, as the U.S. Supreme Court ruled in Torcaso v. Watkins, 367 U.S. 488 (1961), that such state-law requirements violate citizens' rights under the federal Constitution."
(I underlined and bolded)
This also included the Bible-swearing: it has been ruled unconstitutional federally, so no State can force you to do it or penalize you for refusing to comply. This said, if there's a 'jury of peers' witnessing this, it might not be taken so lightly by them. But honestly I have no idea how a trial is conducted in the US, being French and all lol.
I've just seen stuff on TV, series and documentaries and whatnot...
Hope it still helps a bit! And good luck!