I had the same issues with my wife.  But manged to convince her it's no different than any other car.

I took my kid out in my '79 in a booster seat. As folks have said, your kid will be no more or less safe in your Vette than any other vehicle just because it's a Vette. The question isn't so much "should he ride in this Vette?" it should be "how safe is he in ANY vehicle?"   It's not less safe just because it is a Vette, and there is ONLY a front seat in this vehicle.  No air bag is a good thing, in this case.  

Honestly, you or he could be seriously injured or worse in any vehicle depending on how the crash occurs.  If you really think about it, your kid (and you) are much safer just sitting on your couch.  So taking a ride in ANY vehicle offers a degree of risk.  The most you can do is drive as safely and offensively as possible, and hope that no moron rams into you.  But then again, you should be driving that way every day in any vehicle.

If you want to play it safe, yet still give the kid some joy, do what one suggested above and buckle him in for a short ride around the block.

Let us know how it turns out...