"I got the conch."
"Ralph! Stop laughing like that. Look, there ain't no need, Ralph! What's the others going to think?"
Ralph is laughing because he realizes how pointless Piggy's suggestion to use the conch shell is. For most of the novel, the conch shell has symbolized society's rules and order. Those concepts have been slowly eroding away, and now that Jack is in full power and has banished Ralph and Piggy, Ralph sees the conch shell as nothing more than an object. It holds zero power. It is not symbolic of rule and order any more. It's meaningless, and Piggy's desire to have Ralph use the conch shell is ironic to Ralph. Piggy doesn't understand the futility of the shell. Ralph does.
Piggy reacts so strongly because Ralph's reaction scares him. Ralph has been the leader that Piggy put his trust into. Ralph wanted the rules and order that Piggy wanted. Piggy never had the ability to lead like Ralph, and now Ralph appears to be giving up. Piggy reacts strongly, because the world he put faith into is falling apart around him.