I don’t think we (U.S.) would have done this unless and until we were on the same page with SK as to a response . . . if SK does nothing in response at this point then politically speaking, SK President Lee is dead.
Possible responses IMO -
1) cutting off all aid to NK
2) indefinte suspension of 6 party talks
3) strict enforcement of PSI
4) covert military retaliation
I think a few stealth bombers over Pyongyang could sort this out pretty quick.