My tezos are currently baking through a delegated, KTZ account, created from a software-based TZ1 account (created with Galleon). I now have a hardware wallet (Ledger) and want to transfer the delegated account to my new TZ1 account, so as not to interrupt the baking process. Alternative, I would have to stop delegating, transfer the funds to the new hardware-based TZ1 account, create a new KTZ account, and redelegate again. This involve fees (creation of KTZ account) and losing baking time.
It is not possible, as the manager of your KT account would be set the your tz address, and there is currently no way to change this. You should continue receiving rewards for your current address until the new address kicks in, so you shouldn't lose any rewards. I advise that you email your delegation service first though, just in case they have a policy in place regarding this.