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?
Just don't make things so complicated for you just send your Bitcoin and ETH (I assume you men that coin) directly to those exchange so that you won't get any problem if you want to trade.
Also most provably they won't see on where you send those funds. Since what those exchange could see is the public address on where the funds came from, network fee, time stamp and amount also the hash.
I don't know why why you are so conscious with this since less people care about those things