Just because you sing a song from your local area doesn't mean you sing with your normal pronunciation. As a Lancastrian, I sing quite a lot of Lancashire songs with a more "broad" accent that I would never use normally, with pronuncations such as "wheer" (where), "owd" (old), "whoam" (home).

As well as adopting an accent for a particular place, it's also for a particular time, which can only be at best an impression of how people spoke and sang in the days the song originates from. What makes it even more complicated (and interesting) is that we often don't really know when that was!