You can record invoices as normal. No need to worry if they're showing up as Not sent since you send invoices by post anyways. When you receive the actual payment, that's when you mark it as paid.
In QuickBooks Self-Employed (QBSE), we can send the invoices to your email to change the status.
Also, once the invoices mark as paid in QuickBooks Self-Employed (QBSE), they'll default to today's date. Please know that QBSE only offers a simplified invoicing feature. Thus, the ability to modify invoice payments, such as the date, isn't available.