Hi
Any money you will receive will always come as a credit to your Bank, so I do not understanding the logic of not using the Bank Account. This is a very specific case and you have no choice other than to use the Cash Account. If the accounting entry i proposed is not correct, than ask your accounting team as to how they would like to post the accounting entry and based on your business requirement only, anyone can suggest a solution.
Regards
Sanil Bhandari