the closest thing they have to a "modern" ocean going submarine would be the Sinpo* https://en.wikipedia.org/wiki/Sinpo-class_submarine, armed with a single missile that has a range somewhere between 310 miles to a maximum of 1500 miles.
Using Google Earth, Guam and our bases in Japan would be at risk.
The Sinpo is a diesel electric submarine which tend to be quiet when using their electric motors, but at some point the Sinpo would have to come to periscope depth to use run the diesel engines to re-charge the batteries for the electrical motor at which point they become very loud. I have no doubt that there are South Korean submarines, Japanese submarines or US submarines on patrol in the area listening for the Sinpo. If the Sinpo heads east past Japan into the Pacific, it wouldn't surprise me in the least if it had an "accident" and disappeared without a trace.
NK statement is almost certainly intended for internal consumption to show how powerful NK and how wise Fat Boy is to the population of NK.
*Almost all of the North Korean navy is built and intended for coastal use only and much of it is based on late 1950's or perhaps mid 1960's Soviet technology.