Make the sauce: Stir together all of the sauce ingredients in a large bowl. Set aside.
Make the salmon: Combine roughly two-thirds of the sauce and the salmon in a leak-proof bag and refrigerate for at least 30 minutes to allow the flavors to meld. Reserve the remaining sauce.
In a skillet over high heat, warm the coconut oil. Add the salmon fillets to the pan and cook for 2 to 3 minutes on each side. Poke a fork in to make sure it looks cooked through. Remove from the heat and transfer the fillets to a platter.
Drizzle the remaining coconut lime sauce over the salmon fillets. Sprinkle the dill, ginger, lemon zest, salt, and pepper over the fillets and serve hot garnished with the lime wedges and coconut shreds.