Remove drained crab from tin, and place in a mixing bowl. Add remaining crab cake ingredients to the bowl.
Gently mix all the ingredients together with a fork. Mix until incorporated, and then stop. (Do not use a blender or food processor for this step, because you don't want to purée the fish.)
Use a 1 TB measuring spoon (or another small scoop) and scoop the fish cake mix into small balls.
One by one, roll the balls in your hands, and then flatten into small patties 2" across, and about 1/2" thick. You should end up with 12 - 14 patties, depending on the size of your scoop.
Set patties on a rimmed baking sheet.
Refrigerate patties for about 30 minutes.
While the crab cakes chill, mix together all the ingredients for the yogurt sauce. Make sure to taste as you add the cayenne and salt-- use more or less as desired. Put sauce in the refrigerator until it's time to serve.
Move oven rack to the top 3rd of the oven (or about 6" from the broiler). Broil 5 minutes, flip, and broil 3-5 minutes more, until crab cakes are dark and golden.
Remove cakes from pan immediately. Serve while still hot with the yogurt sauce.
Leftovers:Store leftover patties in the fridge, and use within 1-2 days. Use the sauce within a week.Make Ahead + Freeze: Let crab cakes cool, and then wrap individually and tightly with wax paper, plastic wrap, or foil. Store in an air-tight container in the freezer, and use within three months. To reheat, simply unwrap and broil again. Cook until golden, about 5-6 minutes per side, or until the cakes are hot.Sauce should not be frozen.