I was never happy with grilled shrimp until my last cook.
I started with the biggest shrimp I could get. Brined them for a bit, then rinsed, and split the shells along the back with a sharp paring knife.
Tossed them around in some olive oil with creole type seasonings, plus some paprika for color. Let that sit a while, then threaded onto skewers (still in shell).
Grilled on kettle over gentle heat for 2 minutes per side, flip for 2 minutes, etc. until done. Mine were really big, so I think it took about 8 minutes total.
Leaving in the shell helped keep them moist, and splitting the shell let seasoning get in there. It was sort of like what they call barbecue shrimp in New Orleans. Served with spicy cocktail sauce.