That being said, if I want to use any of the said exchanges, I don't have to use any 3rd party wallets in order to do so correct?
As I already wrote, I really don't see any point in using another crypto wallet that the transaction would go to before it ends up on the hardware wallet. This is completely unnecessary and would only create additional costs for you - the only difference between a desktop/mobile crypto wallet and a hardware wallet is that the latter is much safer. Since you have such a device, there is no reason not to use its full potential
