In my opinion the worst thing a person could do in this situation is to force the child to apologize. It will reestablish that what he did was wrong, and, since his baby brother is not able to respond, will make him feel even more guilty. The apology will also be insincere unless it is explained to the child why what he did was wrong. The guilt the child feels will also be translated into a facade of other feelings. I believe it is most likely that the dominant feeling would be even more anger toward his younger brother.
Punishment is also a hard topic to deal with.
Not giving punishment would tell a child it is okay to bully someone weaker. A harsh punishment would only amplify the tension between the siblings. I believe that punishments should be fair, and, when assigning them, be sure that the child being punished understands that he is not being punished because of his brother, but because he knew his actions were wrong and committed them anyway. If the child was ignorant that his actions were wrong, I believe you should explain to them why their action was wrong and suggest another way of with dealing with his situation, oppose to punishment.