Heat butter in a large skillet over medium heat, pan fry the shrimp in shells, adding salt and pepper, until pink on each side.
In a small bowl, combine the next 4 ingredients (honey through oil). Stir in peanuts.
Devein and shell shrimp. Return shrimp to pan and add honey mixture. Heat over low heat until sauce is warm.
Add melon balls and heat until melon is warm, but not mushy.