Season the shrimp with salt and the cayenne; set aside. Using a paring knife, cut the tip off each radish, then make vertical cuts around the radish, being careful not to cut all the way through, to form petals. Place the radishes in ice water to "bloom."
Skewer 3 shrimp each onto twelve 8-inch wood skewers.
In a wide, deep skillet, bring 3 tablespoons water to a boil. Lower the heat and whisk in the butter; add the thyme bunch. Working in batches, add the shrimp skewers to the butter in a single layer, cover and cook for 2 minutes. Flip and continue cooking until pink and just cooked through, about 3 minutes more. Transfer to a platter, discard the thyme and reserve the butter.
Remove the radishes from the water and dry with paper towels. Serve the shrimp skewers and radishes with the butter sauce.