I think you can be pragmatic. Why is calling the External API directly from your API a problem? We are missing several of the details that could make this an interesting question. Also, might be better for the Software Engineering forum.
You have a few options:
A wrapper library just make another layer of indirection that I'm not sure you'd benefit from at this point. If you are worried about keeping the code clean, look at using something like Mediatr so that your controller classes aren't littered with code.
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