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?
Not really.... I think only if you give them your public keys they'll be able to know your seed type or method of generation something like BIP39 or standard ELECTRUM seeds. That aside,if you are sending just your address then all they know is the type of address, better still you should use different address as you receive continuously.
This is to prevent address reuse as it can be used to map out your coins. You can also send coins out of the hardware wallet only it's more complex and you'll need to have a watch only on a device with internet to create and later broadcast the transaction.