The United States Post Office used a nuclear missile to deliver mail in 1959. It worked. They removed the warhead of course.
The ad hoc postal vehicle was a Regulus I, a subsonic cruise missile, that was specially equipped with landing gear. It was fired from the submarine USS Barbero in the Atlantic Ocean to Mayport Auxiliary Naval Air Station in Florida about 100 miles away. Postal personal were on hand with trucks to transport its 3,000 letters — all signed by postmaster general, Arthur E. Summerfield — to the addressees, mostly politicians and dignitaries.
Despite the success, the idea didn’t catch on. At least as of yet.