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?
No the exchange cannot know if you are using a hardware wallet or any other type of wallet.
They can only say that if your address is a segwit or non-segwit address which won't really matter.
Whether it be hardware wallet or hot wallet or any cold storage, none of them give out the wallet details.