I don't see how the U.S. can tolerate a North Korea with nuclear-armed ballistic missiles. If we can't, then we have to make plans to eliminate that threat, using military force is necessary. The Cuban Missile Crisis of 1962 proved that if the U.S. places a very powerful military force in position to act, and if it can convince the opponent it will act if its demands are not met, the opponent may be scared into knuckling under. Part of what made the U.S. plan regarding Cuba work is that its centerpiece was a naval blockade, which did not require any shooting to work. A blockade, being a passive measure, puts the burden on the opponent to decide if he wants to try to raise it by using force.
If China curtailed or cut off its overland trade with North Korea and the U.S. blockaded North Korea's ports, Kim would have to decide whether it was better just to take it, or to start a shooting war he must know would quickly bring an end to his regime and probably to his life. I am convinced that his posturing is just that, and that if he were faced with truly overwhelming U.S. force, backed by a determined will, he would lose his nerve.