I would love a "socially awkward" sim trait but It would be how other sims view that particular sim. Family and friends could experience embarrassment being around you or when you come up in conversation. Certain sims may be hesitant to befriend a socially awkward sim. I'm not sure what would be awkward about the sim but I think this would be a nice way to illustrate some stories.
The shy trait reminds me of the loner trait. loner's can feel tense or embarrassment. They'll go to another part of the house when sims are around.