Preheat a grill to high heat. Toss the shrimp with the chili powder, paprika, salt, and olive oil.
Start the pico: toss together all of the ingredients EXCEPT for the avocado with a few good pinches of salt. Taste and season additionally. Set aside while you grill the shrimp.
When the grill is hot, sear the shrimp on both sides for a few minutes until just barely cooked through. Cook time will depend on the size of your shrimp, but assume about 3 minutes per side for jumbo shrimp.
When the shrimp is cooked, quickly dice the avocado and stir it into the pico with another pinch of salt.
Serve the shrimp over the pico for a light meal, or with chips and toothpicks as an appetizer spread. Enjoy!