Perhaps the best advice for a manager would be to start with a requirements definition that is as complete and accurate as possible. By definition of what a requirements definition is, you, a non-programmer, can do that. Software people have been developing and writing about such things for as long as computers have been around; there are very many books. I do not know what to suggest, especially not for a manager.
Think of a requirements definition as being much like the instructions that would be developed after the system is written. The non-technical description of what the software does is likely to be a good requirements definition. A requirements definition should describe the screens (forms or whatever) as well as the data processed. Describe in non-technical terms how the data is processed.
Only after you have the requirements defined can you proceed to design the system to do it. Otherwise you can waste money developing something that does not work. Software people are very familiar with that.
The article 10 Requirements Traps to Avoid is interesting. It does not explain what requirements definitions are.
If the Python developer is unable to do the required integration then you probably need to hire a developer that can, either as an employee or a consultant. It will probably be better to develop the software using C#. The Python developer might feel threatened. If the Python system is not documented well then this is why management should insist on documentation. Developers often do not want to do documentation and management often does not want to pay for it (pay for the additional time).