In a bowl, combine the shrimp, olive oil, chili powder, paprika, garlic powder, 1 teaspoon salt, and juice from ½ lime. Set aside for 15–20 minutes.
While the shrimp is marinating, soak the wooden skewers for 15–20 minutes.
Assemble the skewers by piercing through the tail of a shrimp, adding the chorizo, then piercing through the other side of the shrimp.
Add a piece of onion, then repeat until the skewers are full.
Preheat the grill to medium heat.
Place the skewers on the grill over direct heat and cook until shrimp is opaque, about 2–3 minutes per side.
In the meantime, add the other half of the lime juice, all of the lime zest, garlic, eggs, and ¼ teaspoon salt to a food processor.
Process to combine.
While the blades are running, slowly drizzle in the vegetable oil, pausing to scrape the sides as needed. Continue drizzling until the aioli thickens, then season with salt, to taste.
Serve the grilled skewers with lime aioli and cilantro, if desired.