I first read LWW as a child, and only saw it as a fairy tale. As a teen I received the whole set of CoN, starting with LWW, and I still didn't get that Aslan was supposed to be Christ until I got to The Magician's Nephew (which was book 6 at the time). Once I realized that, I realized he'd been Christ all along! Now I see even more symbolism with each reading.
My point is that if you don't see the symbolism, they're still great fairy tales. They don't have to be "Christian" if you don't see them that way (although I don't know how you could miss it by the time you get to The Last Battle.)
As for the symbolism of Aslan being like Christ: I agree it's not a perfect analogy; Christ's death did more for us than just save us from the punishment for our sins; but I think it's stretching things to try to deny that Aslan is meant to be symbolic of Christ. There are many other stories where a hero sacrifices himself for someone, but I haven't found any with so many deliberate similarities to Christ. Like Christ, Aslan goes willingly to his death, when he had the power to kill all those who were torturing and killing him; like Christ's death for us, Aslan's death saves Edmund from the terrible consequences of his betrayal; like Christ, Aslan overcomes death and is resurrected; like Christ, Aslan heals people and even brings creatures back from being as good as dead (stone statues); like Christ, Aslan is the son of an even more powerful being we never see (the Emperor-over-the-Sea); and in a later book we even find out that Aslan created the world to begin with! It's one thing for a child to see it as just a fairy tale, but for an adult who knows both stories (Aslan's and Christianity's), I don't know how one could see Aslan as anything but Christ.