Season the flour with salt and pepper; dredge the crabs in the flour, tapping off any excess. In a large skillet, melt 1 tablespoon of the butter in 1 tablespoon of the oil. Add 4 of the crabs to the skillet and cook over moderately high heat until golden, about 3 minutes per side. Transfer the crabs to a low oven and keep warm. Repeat with another tablespoon each of the butter and oil and the remaining crabs.
Wipe out the skillet. Add the remaining 2 tablespoons of oil and heat until shimmering. Add the arugula and season lightly with salt. Remove from the heat and toss quickly to barely wilt the arugula. Arrange the ham slices on plates and top with the crabs. Mound the arugula alongside and serve with lemon wedges.