Place tomatoes, cucumber, avocado, lettuce, black olives, green olives, feta cheese, and carrots in a large resealable plastic bag. Pour in Italian dressing. Seal bag and toss to coat ingredients with dressing.
Microwave spaghetti squash on high for 5 minutes. Cool until easily handled.
Scrape spaghetti squash with a fork and spread onto wraps. Lay turkey and chicken on top. Use a spoon to scoop out ingredients from the dressing onto the wraps. Roll up wraps and slice each one in half.