In a small bowl or measuring cup, stir together the wine and saffron and set aside until ready to use.
Set a large skillet over moderate heat with the olive oil. Once hot, add in the chorizo and cook, stirring often, until browned and crisped, about 2 minutes. Use a slotted spoon to remove the chorizo onto a plate and set aside.
Add the shrimp to the skillet and cook until pink, about 5 minutes or so. Do not over-cook the shrimp as they'll get tough and rubbery. Transfer the shrimp to the plate with the chorizo.
Add the shallot and garlic to the skillet and cook until softened. Stir in the cherry tomatoes and season with a large pinch of salt and pepper. Cook, stirring often, until the tomatoes have softened and begun to burst, about 2 to 5 minutes. Deglaze the pan with the wine and cook until slightly reduced. Stir in the peas and butter and stir until a smooth and silky sauce has formed. Reduce heat to low.
In the meantime, cook the gnocchi in boiling salted water, according to the package directions. Use a slotted spoon to transfer the cooked gnocchi to the skillet. Add a ladleful of the cooking water and stir everything together until evenly combined. Return the chorizo and shrimp and heat until warmed through. Remove skillet from the heat and stir in the arugula. Divide among serving dishes and serve with lemon wedges on the side. Enjoy!