Halfway home. BKK tapped the cooler lid and I said ‘medicine’. Straight through the xray, no need to show documents or even open the cooler.

For anyone in the future: three ice packs (water frozen in a baggie), styrofoam cooler, Two boxes, each containing two pre-loaded syringes,

Further update for anyone doing this: no problem in ICN. The cooler got flagged, pulled, I said it was medicine, she ASKED if she could take a look. Quick consult with the xray operator and they didn't open it or re-xray it.