Glad that you clarified you'll only wear a turtleneck if it's long and drapey — ain't nobody trying to bring back the turtleneck + windsuit / appliqued sweater / graphic vest trend
A drapey sleeveless vest in a light knit can look cool (especially with a chunky pendant necklace)... or give the summer crochet trend a try, like Forever 21's Crochet Knit Sweater, shown in the style board above.