I don't think this is that extra-ordinary of a request. I work in FinTech, and we have routinely had large financial institutions who hire third-party companies

I don't think this is that extra-ordinary of a request. I work in FinTech, and we have routinely had large financial institutions who hire third-party companies in doing code audit and reviews. The key is the third-party companies who do this for their business. I think the key for you is that it needs to be a third-party company that specializes in these types of code audits. I would NOT just hand over source code to the actual company.