A meat cleaver will do horrible damage if it connects, but it is NOT an ideal weapon - it has to be swung back before it can chop down or forward. (Or it has to be swung forward before you swing it backward.) Assuming he has not trained with a broadsword and is attacking you with a continuous figure-8 pattern, the backswing is your opening. In my pre-Taiji days, I used to train with soft sticks: Once you know how, it is relatively easy to get inside the arc of the weapon. So the solution is very, very simple: It is all down to timing and getting inside the arc of the weapon. Happy now?
Oh - then there was another question: Courage. Aye - now that is the REAL question.
A knife with a point is more dangerous as it can stab (without being withdrawn) as well as slash, but it does not look as intimidating.