Exclude Bill from Bill Payment Processing Page

Hello, I have a question regarding excluding certain bills from the EFT Bill Payment Processing page. We have some Vendors that are paid through EFT, but we also pay through credit card occasionally. In these cases, the Bills paid by credit card should not appear on the Bill Payment Processing page. How can I ensure this is done?

I understand there is a Payment Hold tick box, but I would prefer not to use that as the Vendor Bill should be paid, just not through EFT. We also cannot rely on the Bill Payment transaction to be posted before the team who runs EFTs makes the payment through EFT erroneously.