Providing unchecked exception "wrapper" interfaces for an API with checked exceptions
Just accept the fact that the exception is unchecked and move on.

The industry is moving away from checked exceptions: C++ never had them, C# decided not to follow Java in this place, and the latest frameworks for Java are using unchecked exceptions.

Face it, checked exceptions are a nice idea that doesn't work in practice.

As a result, the thing you try in your code, will never pass any code review I'll be part of.