Place the first 11 ingredients in a food processor and pulse until fairly coarsely chopped and well combined. (Do not over mix to a paste; there still should be small, visible bits of shrimp). Transfer mixture to a bowl.
Set out a baking sheet. Spread breadcrumbs on a wide plate. Dampen your hands lightly with cold water. Shape a heaping Tbsp. of the fish/shrimp mixture into a ball. Coat in the breadcrumbs and form into a cake about 2" wide. Set on the baking sheet. Repeat with the remaining fish/shrimp mixture.
Preheat the oven 200 degrees F. Place a large, non-stick skillet over medium to medium-high heat. Add enough oil to lightly coat the bottom of the pan. Cook the cakes, in batches, 3 minutes per side, until golden brown and cooked through. Set on a clean baking sheet and keep warm in the oven. Cook the other cakes.
To serve, arrange cakes on a platter with a bowl of the sweet chili sauce for spooning on top.
Note: Thai-style fish sauce, the chili sauces, and the panko, coarse Japanese-style breadcrumbs, are available in the Asian food aisle.