I, Donald John Trump, do solemnly SWEAR that I will faithfully...
Interestingly the "solemnly affirm" option was only used once--by Franklin Pierce. I expect Trump to have no problem using the standard form of the oath.
In the headline, the word “swear” was being played between its two definitions.
Substituting the phrase, “take the oath of office,” narrows the meaning to one definition. It does not mean that the wording of the oath itself is being changed.