Halve zucchini lengthwise and then cut into 1/2-inch slices. Pour about 3 to 4 tablespoons of olive oil into a large skillet and heat over medium-high heat. Add the zucchini and season generously with salt. Saute until zucchini starts to soften, but is not fully cooked, about 5 minutes. Remove from heat.
Meanwhile, cut the fish into 1-inch cubes for the kabobs and place in a large mixing bowl. Add the tomatoes and remaining olive oil, lemon juice, lemon zest, salt, pepper, and oregano. Toss until fish and tomatoes are well coated. Add zucchini once cooled.
Assemble skewers and pour the remaining marinade over them. Cover with plastic wrap and refrigerate until ready to grill. Skewers can be left to marinate for 30 minutes but no longer than 1 1/2 hours since the lemon juice will start to cook the fish.
Heat a grill or grill pan over medium-high heat.
Grill skewers and baste with remaining marinade, turning once after several minutes on the first side, until fish is just cooked through but not flaking apart, about 7 to 9 minutes total. Serve immediately.