Stir together butter, shallot, zest, lime juice, chili, and salt in a bowl.
If using striped bass, score skin in 3 or 4 places with a thin sharp knife to prevent fish from curling (do not cut through flesh). Pat fish dry and sprinkle with salt. Heat 1 tablespoon oil in a 12-inch nonstick skillet over moderately high heat until just smoking, then sauté 3 pieces of fish, turning over once with a spatula, until golden and just cooked through, 4 to 5 minutes, and transfer to a plate. Sauté remaining fish in remaining tablespoon oil in same manner.