When signing offline transaction are the private keys at any point stored in hardware memory unencrypted as the transaction is signed?
Yes, the keys have to, at some point, be "unencrypted", otherwise the system could not possibly use them to sign the transaction.
That's why I need to be sure as Electrum signes the file that no unencrypted private keys are stored in the computers hardware as I will be going back online with same computer to broadcast the transaction.
Theoretically, after a "hard" restart (ie. power disconnected), the RAM should be, for all intents and purposes, "wiped"...
As far as I'm aware, outside of "lab test" type conditions where you can deep freeze the RAM modules and preserve their state for a few minutes after power is removed, there isn't really a viable "attack" to retrieve the contents of RAM once the machine is depowered.
Or did you mean "persistent" memory like HDD/SDD?
If so, that shouldn't be an issue as the private keys are only kept in RAM for the absolute minimum required amount of time, they're not stored on disk unencrypted unless your wallet file has no password.