Prepare the squash: Slice yellow squash lengthwise to 1/4-inch thickness. Sprinkle with 1/2 teaspoon salt and set aside for at least 15 minutes.
Make the slaw: In a medium bowl, combine oil, lemon juice, garlic, remaining 1/4 teaspoon salt, and pepper and whisk until well blended. Add shredded cabbage and toss until coated with dressing.
Make the cheese spread: In a small bowl, combine goat cheese, cream cheese, and green onions with a spoon until thoroughly blended.
Assemble the wraps: On a work surface, place 2 tortillas and spread each with 2 tablespoons of the cheese mixture. Pat the squash slices dry with a paper towel and place them in the tortillas. Add the avocado, tomato, red-cabbage slaw, and sprouts in layers.