Ok, I checked. While it is true that Kyan lived in the area where some fierce battles were fought and Kyan lived close-by to a strategically important bridge (then again, I guess all bridges have strategic value), the problem in claiming that Kyan died in a cave during the battle of Okinawa is two-fold. First and foremost, the Battle of Okinawa was fought from 18 March to 23 June (according to wikipedia
http://en.wikipedia.org/wiki/Battle_of_Okinawa). Now Kyan, on the other hand, died 20 September 1945 and Japan had already surrendered on 14 August (ok, officially that was the armistice), so why would he still be living in a cave? Just in case? Highly unlikely.
The second thing is that according to Nagamine Kyan was evacuated to the city of Ishikawa, so again the "died in a cave" story sounds more and more like a myth.