Your using windows 7 right ? If yes, that's the problem. I have same issue, and then i found article about fraps doesn't launch on valorant, and they say that is because of windows 7 can't process dx11 well bla bla bla. Then i decided to upgrade windows 7 to windows 10.
And it's work..
Finally i can run valorant with fraps. And i tried to run bandicam too.