The problem is that if you learned it off an in-copyright recording, you will have picked up identifiable quirks the performers added to the piece which will constitute an "arrangement" in the eyes of the law. So you'll have to pay up for the arranger's copyright, which will not be much cheaper than the composer's.

Your only way round that is to find an out-of copyright source and base your version entirely on that, erasing from your mind everything you've heard or read in more recent versions. Not easy, and it will have the side effect that most of your audience will think you're doing it wrong.