Lets say I’m playing in a regular 40/2, SD/1 tourney and at move 28, my opponent’s clock drops to four minutes remaining. He stops writing his notations, and so do I. After move 40, do we have to continue writing down our notations, even though they are incomplete? If we are not using an electric clock, how will we even know when we get the extra hour? Finally, lets say my opponent offers me a draw. I take time to think about it, and I pick up my king to move it, and put it back because I don’t like the move that I was about to make. Am I allowed to accept my opponent’s draw, or must I move my king?
You do not have to continue writing your moves. If there’s no way to continue doing so accurately, then there’s nothing you can do about it.
Touching a piece is the same as declining the draw offer. You can always reoffer the draw, but if your opponent is smart, he/she could insist that you move the piece (and keep insisting until your flag falls). Then he gets the advantage of seeing your move while he considers your offer.