Will there be a way to send the Hawala today tokens to the desktop wallet? It seems that I can only import a private key, which I am wary to do as my HAT are on my Ledger Nano.
Why don't you do like I did - create different ETH address just for HAT and then import private key of that address into the HAT wallet. That way your other coins and tokens are secure in the Ledger Nano S and you can stake your HATs.