Thank God we don’t have to swear on anything to uphold the Bible. However, it’s still dangerous ground. There’s a stereotype when people talk about upholding the Bible. Usually, it means upholding their interpretation of the Bible, which are as wide and varied as there is diversity on the Earth.
So rather, thank God we don’t have to swear on anything to love and care for one another as Jesus has loved us, particularly any law we’ve come up with.