Combine 1/4 cup basil, tomato sauce, 2 teaspoons oil, garlic, salt, pepper and cayenne in a medium bowl. Stir in shrimp; let stand for at least 10 minutes and up to 30 minutes.
Meanwhile, cook pasta in a large pan of boiling water until just tender, 8 to 11 minutes or according to package directions. Drain.
Quarter squash lengthwise and cut into 1/4-inch-thick slices.
Heat the remaining 1 tablespoon oil in a large nonstick skillet over medium-high heat until hot but not smoking. Add the shrimp mixture along with the squash. Cook, stirring, until the shrimp are pink and just barely cooked through, 3 to 4 minutes.
Stir in the pasta and heat, stirring, until piping hot, 1 to 2 minutes. Stir in the remaining 1/4 cup basil and season with pepper.