Depends on the stage of evolution of Bitcoin you're in.
Early Stage: two parties can still trade transactions offline but there's a risk of being double spent against (not completely trustless but not fully trusted).
Second early stage option is: A solution that attempts to prove that private keys to the bitcoin hasn't even been accessed before: https://opendime.com/
Late Stage: Assume Lightning Network connectivity. Since the payment channels in the LN prevent you from double spending coins (attempting to assign UTXO to a different party than your counter party), all you really need to do is issue a channel update and issue a preimage to a hash time locked contract HTLC
AKA, orders of magnitude less than a can of beans.
If for some reason all our computers simultaneously failed without any warning, it would obviously be chaos, but at the end of the day the banks would be in a much better position to recover than anything like Bitcoin. Banks only use computer networks because they are more efficient than the alternatives; Bitcoin requires everyone to be online and does not have any alternatives. The worst thing that would happen if all computers failed simultaneously is that the banks would lose track of everyone's accounts -- a general amnesty for debtors and a big loss for people without debts -- and in the aftermath the banks would just start from scratch using older technologies.
Unfortunately though, it's the network that verifies the absence of double spends, so there's no guarantee of uniqueness.
With the no internet, and limited interbank settlement, I would still bet on the value of crypto over the fiat inflation that would be used to facilitate credit-worthiness.
It seems like this could work, hypothetically, but given the need we have for the currency of our country, it's hard for me to imagine that crypto would hold its value in the face of some kind of massive computer failure.
And if you grant the holder of that IOU the sole right to print and distribute notes representing subdivisions of that debt, you’ll find yourself back at cash!