1. Stir together first 4 ingredients in a bowl; transfer to a large zip-top plastic freezer bag. Add salmon, seal bag, and turn gently to coat. Chill 3 hours, turning occasionally.
2. Meanwhile, stir together yogurt and next 4 ingredients; cover and chill until ready to serve. Soak wooden skewers in water 30 minutes. (Omit if using metal skewers.)
3. Preheat grill to 350° to 400° (medium-high) heat. Scrape outside of cucumbers lengthwise using tines of a fork, scoring skin all the way around; cut into half moons.
4. Remove salmon from marinade, discarding marinade. Thread salmon, cucumbers, and tomatoes alternately onto skewers, leaving a 1/8-inch space between pieces.
5. Grill, covered with grill lid, 5 to 6 minutes on each side or to desired degree of doneness. Serve with yogurt mixture.