Do you think their shorter axe (n12) would be good to take bike camping?
But a too heavy bike is.
I did it bike camping a lot and my advice is, only bring what you absolutely need. Without extra burden, everything is much more enjoyable and you will have more energy to reach the nice spots.
Something like an Eastwing is goong to be a better chopper, but these will split better. Both are useful.
I have a carpenter axe which is very compact and somewhat lightweight, but gave it up because I never had to use it