A headlock is next to pointless
Perhaps it is my choice of words...perhaps I should have used the word choke-hold (shime-waza). If a Judoka manages to get you there, and applies pressure, then you will probably pass-out within a number of seconds. Quite to the point actually. Needless to say I did not wait for that to happen. So in came kote gaeshi. And Judoka don't have the most flexible wrists so the choice was a wise one.