On a cutting board, using the flat side of a chef's knife, mash the garlic and salt to a coarse paste. Add the caraway seeds and finely chop them. Transfer to a large bowl and stir in the chile powder and olive oil. Add the shrimp and toss to coat.
Meanwhile, bring a small saucepan of water to a boil. Add the chorizo and cook over high heat for 5 minutes. Drain and pat dry. Let cool slightly.
Tuck a chorizo slice in the crook of a shrimp and thread onto a skewer; the shrimp should be attached at both ends. Push it to the end of the skewer and repeat with 2 more shrimp and chorizo. Using more skewers, repeat with remaining shrimp and chorizo.
Grill kebabs over a hot fire, turing once or twice, until charred and the shrimp are cooked through, about 5 minutes. Do not over cook. Serve immediately.