You will certainly have issues with copyright, but don't let that deter you.
Be a bit more creative, change the character's names in the story is one idea. You don't have to call him 'Rudolph.' you could always invent a new myth. Go for originality and people will notice more. Don't bother with fan fiction, it won't really get you anywhere. Once you're done you could always take advantage of self-publishing and who knows what that will lead too.