Edmund is waiting, and he has no reason to hide. He knew that no matter what, Peter would show up to either defend himself or his belongings. Edmund would have done the same.

Granted, he doesn't realize he's cursed, either.

"Of course I'm sure," Edmund replies breezily, his own sword ready for a fight. He'll keep his, naturally. He won't give up either his own sword or his own crown. This isn't a tradeoff. Edmund wants everything, he has never wanted everything quite so badly before.