According to a guide, if Knuckles dies, it should point you to another bandit ("newly promoted leader") who will give you a reward. Try looking for a bandit who appears as a star on the minimap. It should also be pointing towards said bandit if that mission is set as your active mission. Otherwise, it just might be bugged, which would be quite rare. You should also save regularly and keep multiple saves just in case.
It's also not the "first mission". CoP is open-ended with multiple side missions to complete as you see fit. Your real first mission is to find and investigate the Stingray crash sites.
Besides, what loser joins Bandits anyway? Help out your fellow Loners instead.
(Not meant to be offensive!)
I just loaded a savegame. This time it was "Crybaby" who died. So nothing of value was lost. And... you can finish the game without joining the bandits???