Welcome to the forum, Kristine!
Before you dive in, you should search for stingray on this site. Look at a few people's projects, and you'll see the trouble they've run into. Stingray is one of the hardest leathers to sew nicely, and it's expensive, so that will hopefully save you a lot of money and headache.
I've never worked with stingray, partly because of the above. However, if I had to, I'd do inlay on top of a piece of veg tan to eliminate the edge problem and hide the stitching line. But that's probably not the look you're hoping to achieve.
I know another member was researching clutch stiffness recently (http://leatherworker.net/forum/index.php?showtopic=62432&hl=kymberly), maybe she's figured out something that would work.
As you can see, she didn't get much help - not many clutches on this forum, and the ones I've seen are soft. However, I'd love to see your solution to the problem!