I would say don’t catch the exception if you really can’t handle it. And logging isn’t considered handling an error. Better to bubble it up to someone who can by throwing the exception.
If you must return a value, and null is the only sensible thing, there’s nothing wrong with that. Just document it and make it clear to users what ought to be done. Have a unit test that shows the exception being thrown so developers coming after you can see what the accepted idiom needs to be. It’ll also test to make sure that your code throws the exception when it should.