You can’t directly create an unsigned Overwinter transaction and then have the TREZOR sign it, because the Overwinter SignatureHash function is different, and the old firmware doesn’t know about it (so would try to sign the transaction with the Sprout SignatureHash function). However, the signing algorithm itself is unchanged, so you may be able to work around this if TREZOR has the ability to sign any arbitrary message hash (i.e. just the signature operation). I suspect you can’t leverage an arbitrary-message-signing feature though, as that likely hashes the message internally regardless of its length, whereas you would want to calculate the Overwinter SignatureHash and then pass that in without further modification.
tl;dr I do not know whether it is possible with the pre-Overwinter version of the TREZOR firmware.
General advice to hardware wallet users: if you lose access to the backup of your seed words, you should transfer your funds out of the hardware wallet immediately (and then reset it with a new seed), because you could lose access to your funds in the same way as above, as well as if e.g. your device broke.