OK, again in the spirit of it......"before they strike blows". I wouldn't have that happen at INit 1, (or when the character swings) cuz as you pointed out, that would be dumb. It would be after assault moves, overwatch, any dangerous terrain tests, all that.
I;m basically going for just the most OBVIOUS, immediate interpretation. Remember, they're neither engineers nor programmers over there.
I think whether it was before or after challenges were declared would be open to question. Probably after. Just before the initiative order.