If using bamboo skewers, soak skewers in hot water at least 30 minutes. Prepare outdoor grill for direct grilling on medium.
In large bowl, combine sugar, paprika, chili powder, cayenne, 3/4 teaspoon salt, and 1/2 teaspoon freshly ground black pepper. Rub mixture between fingers to break up any lumps of sugar. Add salmon and squash and toss to evenly coat with spice mixture.
Thread squash slices, 2 at a time and alternating with salmon, onto skewers. Place on hot grill grate and cook 9 to 11 minutes or until salmon turns opaque throughout, turning occasionally.