I am a lefty and I hold my pencil with my thumb, resting on my ring finger with my pointer and middle finger resting/guiding it on the top. When I was little it wasn't so much how I held my pencil that was an issue but rather how I held my paper to write on it! (sideways, opposite the way the teacher thought it should go)
In terms of being completely left or right handed, that should not be an issue because it is very common for someone to be left handed, but "right sided" or visa-versa. I am left handed for everything except putting - I am definitely a right handed putter. DD8 is a righty for eating, writing, drawing and things like that, but we found out last year that she is athletically a lefty.
It is more complex than saying that a person is right handed or left handed, it has to do with how they visually perceive things.
