Is there a 'better' choice? Twilight vs general anesthesia for a 'skin pinch' procedure?

This type of procedure can be performed using only local anesthesia, at most twilight. We never use general anesthesia for any kind of eyelid surgery. I would prefer local if your surgeon is willing to do it this way.

While general anesthesia is considered safe, it is not perfectly safe.  Things can happen.  Intravenous sedation performed for "twilight" anesthesia is a level where you are not aware but do not require a endotracheal tube to maintain your airway.  It is generally less stressful to the body.  I agree with others that it is possible to do this type of procedure under local anesthesia.  I would caution you about a skin pinch.  These often are not a skin pinch but a skin and muscle pinch that results in a weakening of the lower eyelid with post operative compromise of the lower eyelid. 

For a simple procedure, why go the route of general or twilight anesthesia? A local anesthetic with oral sedation should do fine.