Can I not just create the transaction on the offline computer?
If you know which inputs you are going to spend, and you know what the Txout-script (also known as the scriptPubKey) is for each input, then you can just create the transaction on the offline computer.
If you don't know how to do that, then it is just easier to use an online wallet that can look that information up in the blockchain for you and build the transaction. IT saves you a lot of effort and helps reduce the opportunity for mistakes.
