I just give them my driver's license and carry permit along with my registration and proof of insurance all at once. In the one in a million chance the a trigger happy cop notices my gun under my knee I don’t want to get shot. I’m not trying to start a debate but I’m just not that worried about telling the cop I’m legally armed.
Why in the world do you have your gun under your knee? If I see that on my approach we’re going to be having a very different interaction and subsequent conversation.