Acoodring to wikipedia:
The W19 nuclear system was adapted into a nuclear artillery shell for the US Navy 16 inches (410 mm) battleship guns, the W23. Production of the W23 began in 1956 and they were in service until 1962, with a total of 50 units being produced.
The W23 was 16 inches (410 mm) diameter and 64 inches (160 cm) long, with a weight given variously as 1,500 or 1,900 pounds (680 or 860 kg) in reference sources. As with the W19, yield was 15-20 kilotons.
Do any existing sources detail if the nuclear-ship launched shells were intended as shore bombardment rounds, for use against other ships (or fleets) or for other purposes? Under whose command would these weapons have been used in the short timespan they where in service?