Cook artichoke hearts in a large saucepan according to package directions. Add shrimp the last 3 to 4 minutes of cooking; cook until shrimp turn opaque and artichokes are tender. Drain well. When cool enough to handle, halve any large artichoke pieces. Combine artichokes, shrimp, and red pepper strips in a medium nonmetal bowl.
Combine vinegar, oil, green onion, garlic, oregano or basil, salt, dry mustard (if desired), and pepper in a screw-top jar. Cover and shake to combine. Pour over artichoke mixture, tossing gently to coat. Cover and chill for 2 to 4 hours, stirring occasionally.
To serve, drain mixture and transfer to a shallow serving bowl or platter. Serve with a slotted spoon or picks. Makes 15 servings.