Prepare the grill for medium heat.
In a small bowl, mix together the salt, paprika, cumin, chili powder and oil.
In a medium bowl, gently rub the spice blend into the salmon pieces. Thread the salmon onto skewers. Set aside.
In another medium bowl, mix together the cucumber, red onion, hot pepper and cilantro. Gently mix in the avocado. Pour 1/2 of the lime juice into the salsa and add salt to taste.
Grill the salmon, turning once or twice, until the fish is opaque throughout, for 5–7 minutes. The fish will cook quickly.
Drizzle the remaining lime juice over the salmon and serve with the avocado–cucumber salsa.