I'd say CSX3170 is a contender for the title. Check out this and several other threads from the owner who goes by the same name here on CC. His original Cobra has been treated to a long list of suspension mods and adjustments with goal of optimizing slalom/autocross performance:
CSX3170 at Scottsdale Goodguys
The best handling Cobra is likely going to be one whose owner has invested some time, research and $$ into setting it up in a way that mitigates and/or leverages the physical traits inherent to the car.
Out of the box best handling Cobra? There are brands like the XCS Cobra in the UK that take the already sharp handling Dax De Dion chassis to a whole 'nuther level with their patented camber compensation and anti-roll (CC & AR) technology at all four corners:
XCS Designs
Road test report here:
https://www.youtube.com/watch?v=YaxCu-OmnqI
Absolute Pace in Australia build an accurate looking Cobra replica with an aluminum semi-monocoque chassis and inboard rocker suspension system. No hard data on handling performance though:
http://www.absolutepace.com/images/brochure_pace427.pdf
There are others - like the ground-hugging JBL with its race bred chassis and suspension, which was billed as more "Cobra-inspired" than an actual replica. Not sure how easy it would be to acquire one of those.
Be careful with that street racing thing though - no matter how great a handling Cobra you end up building or buying. We've seen some very unhappy endings to that story over the years...