For the sauce: Grate the cucumber on the large-holed side of a box grater. Place the grated cucumber in a fine-mesh strainer and drain for a minute or two, pressing out as much liquid as possible.
Stir together the grated cucumber, yogurt, oil, lemon juice, garlic, parsley, salt and pepper in a medium bowl. The yield is about 1 cup. Cover and refrigerate until ready to use (and up to 4 days).
For the burgers: Place the bread in the food processor and pulse to make fine crumbs. (The yield should be about 1 1/2 cups.) Transfer them to a large mixing bowl.
Cut the salmon into large chunks, then transfer to the food processor; pulse until chopped but some pieces still remain visible, 10 to 15 pulses; add to the bowl with the bread crumbs.
Add the scallions, celery, dill, Dijon mustard, lemon juice, egg white, salt and pepper to the bowl, mixing to combine. Form this mixture into 4 equal patties and place them on a plate. Cover and refrigerate for 10 minutes to set.
Preheat a grill pan over medium-high heat. Once it is hot, grease it with cooking oil spray; add the salmon patties and cook for about 3 minutes per side or until just cooked through.
Serve with the sauce, on whole-grain buns or with lettuce leaves (to use as wraps).