Start by preheating your oven according to the phyllo shell package instructions and arranging the shells on a baking sheet. While the oven heats, mince your garlic, slice the green onions, chop the fresh dill, shred the Swiss cheese, and measure out all remaining ingredients into small bowls. Place the phyllo shells in the oven to bake according to package directions (typically 5-8 minutes until golden and crispy). This parallel timing means your shells will be ready right when you need them.
Melt the butter in a large skillet over medium-high heat. Once foaming, add the minced garlic and cook for about 1 minute, stirring frequently, until fragrant but not browned. Add the shrimp pieces and cook for 3-4 minutes, stirring occasionally, until they turn pink and opaque throughout. Transfer the cooked shrimp to a plate and let cool for a few minutes—this prevents the shrimp from cooking the mayo when mixed together. I find letting it cool completely ensures a better texture in the final salad.
In a medium bowl, combine the cooled cooked shrimp with the mayonnaise, shredded Swiss cheese from Step 1, green onions from Step 1, lemon juice, dill seasoning, smoked paprika, and fresh dill from Step 1. Fold everything together gently until well combined, being careful not to break up the shrimp pieces too much. Taste the mixture and add salt as needed—I typically add about 1/4 teaspoon and adjust from there. The acidity from the lemon juice really brings out the dill and shrimp flavors, so don't skip it.
Remove the baked phyllo shells from the oven and let them cool for just 1-2 minutes so they're still warm but safe to handle. Spoon the shrimp salad mixture generously into each phyllo cup, dividing it evenly. Serve immediately while the shells are still crispy—they start to soften once filled, so don't prepare these too far ahead.