If you are downloading the Exodus wallet from their official website (linked) then there should not be a virus. It may just be your anti-virus software doing that because it's crypto related, but since I am not seeing what you are seeing, I do not want to give you any advice and then you wind up infected. Check the URL, and make sure it is legit.
Personally I would not keep my EOS on an exchange since I like to control my private keys, especially in a situation like this where things are changing, but that is just me.
RE: Register Your EOS Before June 1 or You Could Lose Your Tokens - Exodus Wallet EOS Registration Instructions