Zahavasdad (sorry I couldn’t reply earlier)
Inaugural Balls are not a minhag medinah, but a minhag of the particular President, and scheduled at his whim. There is no requirement to hold the ‘official’ inaugural ball the nigt of the swearing in (or to even have one).
“The first Inaugural Ball (for George Washington) was held a week after the Inauguration. Presidents have cancelled inaugural balls for various reasons. Franklin Pierce, who was mourning the recent death of his son in 1853, Woodrow Wilson, who in 1913 felt that inaugural balls were too expensive, and Warren G. Harding, who in 1921 wanted to set an example of simplicity, all opted to end the custom of inaugural balls. Private parties known as “charity balls”, were held during the second inauguration of Calvin Coolidge in 1925, for Herbert Hoover in 1929, and especially during the depression and World War II era inaugurations of Franklin D. Roosevelt in 1933, 1937, 1941, and 1945.”
The new President could have chosen any date he wanted for the ball (from January 20th on) or no ball at all.