Combine first 3 ingredients in a large bowl; let stand 5 minutes. Stir in 2 cups flour, 2 teaspoons olive oil, and salt to form a soft dough.
Turn dough out onto a lightly floured surface. Knead for 5 minutes or until smooth and elastic, adding enough remaining flour to prevent dough from sticking. Shape into a ball; place in a lightly greased bowl, turning to grease top. Cover and let rise in a warm place (85°), free from drafts, 40 minutes or until doubled in bulk.
Punch dough down; divide into 6 equal portions, and coat with olive oil. Roll each portion into an 8-inch oval, and set aside on lightly oiled baking sheets.
Brush grill rack with oil (lightly to avoid flare-ups) over high heat (400° to 500°).
Place dough on rack, and grill for 2 minutes or until bottoms of crusts are lightly browned and tops begin to puff. (It's easier to prepare pizzas in batches.) Turn crusts over; top evenly with salmon, capers, and cheese. Close grill lid, and grill for 1 to 2 minutes or until cheese melts and crusts are golden brown.
Sprinkle each pizza with 1 teaspoon fresh dill and juice of 1 lemon wedge; serve immediately.