Take a look at
I'm sure they can supply something lightweight that will fill the bill.
I did a lot of backpacking back in the day and I sure understand the weight thing!
Well, thinking about it, you're certainly at the opposite ends of the sharpening spectrum with an axe and a razor. Also take a look at
They have a lot of sharpening equipment: the founder literally "wrote the book" on the sharpening of blades and tools.
Edited by MikeLM - 1/13/15 at 11:44pm
My comments are for the Continental US.
An Axe usually is sharpened by file. A straight razor by strop. There's not a lot of need for sharpening in a modern backpacking scenario. And no place for an axe. Too big, too heavy, too much impact. hatchet is overkill as well. Even the wood and twig stoves can be easily fed without the weight and bulk of an axe with a simple batoning technique on a light fixed blade, 3-4 inches of blade is plenty. Bark River Knife and Tool makes a number of hard working blades that can do this sort of work with ease.
And I'm puzzled by why you'd take a straight razor in a backpacking situation. Again, there are simpler, lighter, more compact solutions or you can skip shaving entirely.
For back packing, I'd probably go with a compound loaded section of carboard, Frequent touch ups rather than letting anything get dull.
But again, very little edgework is needed in modern backpacking. A small folding swiss army knife is more than capable and easily sharpened on the cardboard. I'm a fan of the Farmer model which includes a surprisingly capable saw blade for handling many of the things you might think you need the axe for on wood up to 1 1/2 inches.
If you're wanting to practice primitive skills, on most public land, an axe is worthless as the wood gathering and use rules prohibit much of the use of an axe. You'll need to go on private land. And in this case where a lot of edge work and maintenance was the plan, i'd probably go with a DMT diamond system in the diafold style. And still have the compound loaded cardboard for fine blade edges.