Can I use a seed obtained from an exchange in early 2014 to import my private key into either a Trezor or Ledger Nano S hardwallet?
No, I don’t believe that you can – but it’s a good thing. The purpose of a hardware wallet is to generate and store a private key in an entirely offline, self-contained and secure manner. During normal operations, that private key will never leave the hardware wallet (the exception is via the backup seed phrase, which you must copy exactly and store securely).
Having the private key never touch directly interfacing with anything hackable (like your PC or phone) is what makes hardware wallets secure. Only the key’s output (like signing to authorise Bitcoin transactions, for example) ever reaches your device.
You should just send your coins from 2014 to an address associated with your hardware wallet. That way, those coins will be secured.