This part is incorrect. I've handed completed assassination missions in successfully well after the 24hr timer would have expired. The timer disappears after you've killed the target.
Edit: looks like Stealthie has already mentioned that.
In that case, the 24 hour timer is irrelevant and should probably be removed from the mission description since the mission timer will only start once you accept the mission, and will essentially end at the end of the window of opportunity, so the 24 hour bit means nothing at all.