I don’t think your scenario is all that realistic. Someone takes your wallet, and then tries to KILL you because you’ve seen his face? With his bare hands? Killing ANYONE besides small children and the elderly with one’s bare hands isn’t easy, clean, or quiet no matter how out of shape or overweight the victim is. In a life to death adreanline pumping kind of encounter, you are just as likely to kick him in the nuts and disable him as he is you, the ability to run triathalons probably isn’t going to help either of you, and even if he does win, chances are you would have dealt him a few grevious injuries before going down, which won’t help his chances of escaping the authorities later.
Assuming your assailant isn’t particularly bright or well prepared, it’s a crapshoot really. Match the other guy in agression, fight dirty but remeber he will be doing the same, scream like a banshee, which will boost your confidence, alert passerbys, and unerve your opponent. SInce you seem to have a much greater stake in this than he does (life vs the $10 in your wallet) chances are he will give up and run for it before you.