Add wood chips to grill according to manufacturer’s directions.
Using long-handled tongs, moisten a paper towel with cooking oil and lightly coat the grill rack. Thread shrimp onto two metal or soaked wooden skewers. Grill, covered, over medium heat for 5-8 minutes or until shrimp turn pink, turning once.
Meanwhile, cook fettuccine according to package directions. In a large skillet, saute broccoli and mushrooms in oil until tender. Add garlic and salt; cook 1 minute longer. Add wine, stirring to loosen browned bits from pan. Gradually stir in cream. Bring to a boil. Reduce heat; simmer, uncovered, for 10-12 minutes or until thickened.
Drain fettuccine. Add to sauce mixture with shrimp. Cook and stir until heated through; gently stir in tomato.