Rereading the original post, like many subjects Cobra, there is not "a single" answer.
The first Cobras used a flip up little chrome plated cover (Triumph something I believe) and a separate tool to put through the hole exposed when the cover was raised to work the latch mechanism below. I never heard of anyone enjoying using them. Once several decades ago I watched a very 'excited' Cobra owner fumble around the cockpit looking through the glove box and door pockets looking for his latch tool while electrical smoke was escaping from the closed engine bay. Fortunately he found the "key", got the bonnet up, and disconnected the battery before any damage that couldn't be repaired on the spot before day's end was done.
Shelby race cars got custom fabricated "tear drop" handles permanently mounted. The first ones were just painted black as I understand it. Soon they were upgraded to chrome plating and came into use on street cars also.
The common Wilmot Breeden handles people associate with Cobras replaced the hand fabricated Shelby pieces and were used from then on. I haven't seen any in a long time but there was another British application that used keyed lock cylinders in the handles and in the 1970s and early 1980s I would occasionally see one or both handles on a Cobra/427 Cobra owner upgraded to the locking handles. Photos of the original hardware samples from a CSX24XX car damaged badly decades ago.