There is absolutely no meaningful agreement about what the more limited range of such missiles would be. The Washington Post, for example, quotes a possible range of 2,175 to 2,672 miles in its July 5 edition. Other sources quote maximum ranges of 3,500, 4,000, and 5,000 kilometers. All are sheer guesswork, and all ignore the fact that missiles do not have maximum ranges; they have range-payloads. If you do not know (or at least state your assumption about) the weight of the warhead or payload, your guesses are undefined and irresponsible rubbish.
Accordingly, until better data are available, the main risk seems to be that North Korea is beginning early testing of a missile that could throw the equivalent of a rock at Alaska. Even in the worst case, it would be able to launch a small fission nuclear weapon with great inaccuracy and unreliability at Alaska, and just possibly Hawaii or the upper northwest corner of the U.S. Given its history of testing to date, it is probably around five years away from even this operational capability, although shorter times are all possible.
What there is, I’d wager, is near unanimous agreement that North Korea has the capacity to hit Japan with nuclear armed ballistic missiles either now or in the very near future. Japan has a couple of reasons to worry about this. First, the North Koreans will undoubtedly target Japan in the assumption that the prospect of the destruction of Tokyo will deter the US almost as much as that of Los Angeles. Second, this assumption may not hold. Although it’s virtually impossible to imagine a US president making a well-reasoned decision that attacking North Korea would be worth the destruction of Tokyo, it is certainly conceivable that US policymakers will think about the five years prior to a reliable North Korean ballistic missile threat as a window of opportunity. The threat of nuclear attack, rhetorically and psychologically, is likely to be less acutely felt when the target is not American. Consciously or no, American policymakers might be more willing to take risks when Tokyo rather than LA is at risk.
Obviously, this would be of concern to Japan, and I can see why the Japanese would seek their own, independent means of dealing with North Korea.