Since there's currently no answer here, I thought I'd do some digging. I haven't been able to get an exact number, but we can at least have a little fun getting an approximation.
In Boult's obituary in the New York Times, Edward Rothstein highlights Boult's
a baton that was nearly the length of his arm.
And in an activity created by the Forensics Department at Rice University, we see that
a person’s height can be estimated using the lengths of the long bones of the body—the femur, tibia, and fibula in the leg, and the ulna, radius, and humerus of the arm.
So, let's try it! The height of a Caucasian male is estimated to be the length of the ulna times 3.76 and with a further 75.55 cm added. Regarding the radius, it's 3.79 times the length, plus an additional 79.42 cm. And as for the humerus, it's 2.89 times the length, plus 78.10 cm.
Solving these equations, we see that 6 feet (182.88 cm) suggests an ulna length of 28.54 cm (11.24 in), a radius length of 27.29 cm (10.74 in), and a humerus length of 36.26 cm (14.28 in). Averaging the ulna and radius lengths and combining them to the humerus, that's an arm length of 64.18 cm (25.27 in).
So our current best guess is that his wand length approached 25 inches, about the length of Harry Potter and Lord Voldemort's wands combined.