Cook the spaghetti according to the package instructions, reducing the cooking time by about 1 minute for a firmer texture (al dente). Drain and rinse with cold water. Drizzle with a little olive oil to prevent sticking, then refrigerate until cool.
In a large mixing bowl, combine the cooled spaghetti with the cherry tomatoes, cucumber, salami or pepperoni, green bell pepper, red onion, and black olives.
Whisk together the Italian salad dressing ingredients if making from scratch, or shake the store-bought dressing well. Pour the dressing over the salad ingredients and toss to coat evenly.
Sprinkle with grated Parmesan cheese and paprika, and season with salt and pepper to taste. Mix gently to combine all the ingredients.
Cover the salad and refrigerate for at least 2 hours to allow the flavors to meld. Serve chilled.