As the system was not designed to work that way, there may be a some work arounds or perhaps input from others. Once you create an invoice, you can't delete it, even a draft. One thought would be create an email address that you could send the invoice to, you would then have a record of the transaction. By using a specific email address, you would know that the transaction was cash, check, etc. and you could search on that address. Not really ideal but, could work as there's no categories for cash, check, etc. Just a thought as maybe there is a more creative method.
