I believe that it is settled law that Federal LEOs can carry without interference from State and Local Law Enforcement. SCOTUS made that decision in a California case were state LEO arrested a Federal Marshal. I don't remember the Case.
If POTUS wishes to carry I don't think it would violate any law. Since his carry would involve security he can issue an unpublished Executive Order and not advise anyone.
Historical Note: Andrew Jackson shot a guy off one of the Balconys of the White House. Old Hickory was a great shot and notorious duelist.