No, if the transfer is offline, there can be no guarantees that the same person didn't try to double spend by transferring the same funds to someone else (unless you involve a trusted third party).

I assume the question is “can you do all the transaction signing offline” before actually posting it.

E.g.

1. Pull current BTC hash/tree/whatever-is-needed-in-a-transaction copy onto usb stick

2. Transfer that data to machine with account key via a usb stick or some other connection that has no external communication

3. Use that information to generate the transaction

4. Copy the transaction to the connected machine - a photo of the transaction text on screen even :)

5. Push the transaction out

6. Destroy the intermediate storage devices

Would that work?

No, that's not what the question was. The parent poster specifically said "you don’t know if they kept a copy of the key. But is there some mechanism whereby it could be guaranteed that you have the only copy?" In your example the account key on the usb stick is not guaranteed to be the only copy, and thus, there is risk of the sender double spending that money.

That’s basically what a hardware wallet like ledger or trezor is.

Unless the seed was used elsewhere / in another similar device.