If paper and pens still exist in this world, then physical invoices can be used as transaction records during the blackout.
An invoice is a document that records all info related to a transaction, such as the agreed price, the items sold, and when the payment needs to be made. Today, both electronic and physical invoices are used for transaction where payments are not immediate(source: I develop transaction software), such as large-scale purchases of bulk goods. They are typically issued by the seller to the buyer, so many businesses would already be familiar with generating invoices.
So, all that is needed to temporarily replace the electronic economy is a steady supply of paper and pens. The seller would write the goods being sold, the amounts, the prices, etc., and the buyer and seller would both sign/somehow mark the invoice in order to authenticate it. Two copies, one for the buyer and one for the seller copy, would likely be made. When the electronic systems come back online, these invoices would be used to ensure that the proper money transfers are made.