When you move money into the offline system, you could specify a denomination. The denomination is used as part of the key generation system. There would be different addresses for each coin size.
If you want to send 50.12 BTX and have "coins" of 1BTC, then it would create a transaction and send 1BTC to 50 addresses and the 0.12BTC back as change.
To spend the coins, you still need the offline computer. However, the source address would be a known public key for a denomination, so the offline wallet would be able to say what the input value is, without needing aux-data.
If you wanted to be even fancier, you could generate a series of three addresses.
TX-1:
TX-2:
TX-3:
TX-4:
All the public keys could be computed by both computers. The private key for address-1 (and maybe address-3) needs to be computable by the online computer.
Once TX-1 and TX-2 are completed the money is secure.
If the online computer knows the public key for address 3, then it creates a vulnerability on spend. If the computer has been compromised, then it could direct the output to a false address.
The offline computer can compute TX-2, so can compute TX-3. It just needs denomination and id number of the coin(s) to spend.
The offline computer could handle TX-4 too, if told the address.
However, ideally, the info transfer should be offline to online computer only. Also, if you only take 1-2% of the total in the store out at a time, then the risk is kept low.