Let me refine the question a bit lol. Can I use any exchange that I have BTC and ETC on and The hardware wallet supports BTC and ETC?
when I give my crypto exchange my public address of my wallet to do a transfer , does the exchange know from the address any info like the wallet I am using....or?
Your BTC or ETH wallet address is only linked to the blockchain not to a specific hardware or even software wallet. So the answer is obviously no. Reason been that no exchange sees the type of wallet used by mere looking at the address. As long as your hardware wallet supports the coin and you use the correct address type, you can safely withdraw from any exchange to the wallet.